MATE CCSS II/Tema 3-Sistemas de ecuaciones Ariketa_1_1 Discute y resuelve los siguientes sistemas, utilizando el método de Gauss:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»-«/mo»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mrow»«/mstyle»«/math»

Rango(A)= {#1} {#2} Rango(A^*)= {#3} {#4} nº de incognitas

SISTEMA {#5}

Solución: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»x«/mi»«mo»=«/mo»«/mrow»«/mstyle»«/math» {#6} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«mo»=«/mo»«/mstyle»«/math»{#7} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»z«/mi»«mo»=«/mo»«/mstyle»«/math»{#8}

]]> 8.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_1_2 Discute y resuelve los siguientes sistemas, utilizando el método de Gauss:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mn»4«/mn»«mi»y«/mi»«mo»+«/mo»«mn»2«/mn»«mi»z«/mi»«mo»=«/mo»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Rango(A)= {#1} {#2} Rango(A^*)= {#3} {#4} nº de incognitas

SISTEMA {#5}

]]> 8.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>*</mo><mi>z</mi><mo>+</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>z</mi><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_1_3 Discute y resuelve los siguientes sistemas, utilizando el método de Gauss:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Rango(A)= {#1} {#2} Rango(A^*)= {#3} {#4} nº de incognitas

SISTEMA {#5}

]]> 8.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_10 Dos amigos invierten 20.000 € cada uno. El primero coloca una cantidad A al 4% de interés, una cantidad B al 5% y el resto al 6%. El otro invierte la misma cantidad A al 5%, la B al 6% y el resto al 4%.Determina las cantidades A, B y C sabiendo que el primero obtiene unos intereses de 1050 € y el segundo de 950 €.

]]> 1.0000000 0.3333333 0 0 Cantidad-A=#x1Cantidad-B=#y1 Cantidad-C=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>20000</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo>.</mo><mn>04</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>06</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>1050</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo>.</mo><mn>05</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>06</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>04</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>950</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5000.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5000.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10000.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi>A</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>C</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi>B</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>C</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi>C</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_11 Una tienda ha vendido 600 ejemplares de un videojuego por un total de 6.384 €. El precio original era de 12 €, pero también ha vendido copias defectuosas con descuento del 30% y del 40%. Sabiendo que el número de copias defectuosas vendidas fue la mitad del de copias en buen estado, calcula a cuántas copias se le aplicó el 30% de descuento.

]]> 1.0000000 0.3333333 0 0 Copias-a-las-que-se-le-aplicó-30%-descuento=#x1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>600</mn></mtd></mtr><mtr><mtd><mn>12</mn><mo>*</mo><mn>0</mn><mo>.</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn><mo>*</mo><mn>0</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>12</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>6384</mn></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>p</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi>s</mi><mo>-</mo><mi>a</mi><mo>-</mo><mi>l</mi><mi>a</mi><mi>s</mi><mo>-</mo><mi>q</mi><mi>u</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>s</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>l</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>a</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>ó</mi><mo>-</mo><mn>30</mn><mo>%</mo><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>c</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>o</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_12 Un cajero automático contiene 95 billetes de 10, 20 y 50 € y un total de 2000 €. Si el número de billetes de 10 € es el doble que el número de billetes de 20 €, averigua cuántos billetes hay de cada tipo.

]]> 1.0000000 0.3333333 0 0 Billetes-de-10€=#x1Billetes-de-20€=#y1 Billetes-de-50€=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>95</mn></mtd></mtr><mtr><mtd><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>50</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>2000</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>y</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi mathvariant="normal">i</mi><mi>l</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mn>10</mn><mo>€</mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>B</mi><mi mathvariant="normal">i</mi><mi>l</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mn>20</mn><mo>€</mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>B</mi><mi mathvariant="normal">i</mi><mi>l</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mn>50</mn><mo>€</mo><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_13 Encontrar un número de tres cifras que verifique las siguientes condiciones:

La suma de sus cifras es 24.
Si permutamos la cifra de unidad con la cifra de decena, el número obtenido es nueve unidades menor.
Si permutamos la cifra de decena con la cifra de centena, el número obtenido es 90 unidades menor.

]]> 1.0000000 0.3333333 0 0 El-número-pedido-es=#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>24</mn></mtd></mtr><mtr><mtd><mn>100</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>z</mi><mo>+</mo><mi>y</mi><mo>+</mo><mn>9</mn></mtd></mtr><mtr><mtd><mn>100</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>z</mi><mo>+</mo><mn>90</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>x1</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>y1</mi><mo>+</mo><mi>z1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>987</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>l</mi><mo>-</mo><mi>n</mi><mi>ú</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>o</mi><mo>-</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>o</mi><mo>-</mo><mi mathvariant="normal">e</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_14 Calcular el valor de m para que el siguiente sistema tenga soluciones distintas de la trivial

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mi»m«/mi»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«mi»x«/mi»«mo»+«/mo»«mi»m«/mi»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Calcula las soluciones propias del sistema para los valores de m que has encontrado.

m = {#1}

Sol: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»x«/mi»«mo»=«/mo»«/mrow»«/mstyle»«/math»{#2} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«mo»=«/mo»«/mstyle»«/math» {#3} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»z«/mi»«mo»=«/mo»«/mstyle»«/math»{#4}

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi>x</mi></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><reals/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_15_1 Discutir y resolver en función del parámetro m el siguiente sistema

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»+«/mo»«mi»m«/mi»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Empieza con el valor menor de m.

Si m = {#1}, entonces , Rango(A)= {#2} {#3} Rango(A^*)= {#4} {#5} nº de incognitas

SISTEMA {#6}

Sol: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»x«/mi»«mo»=«/mo»«/mrow»«/mstyle»«/math»{#7} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«mo»=«/mo»«/mstyle»«/math» {#8} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»z«/mi»«mo»=«/mo»«/mstyle»«/math»{#9}

Si m = {#10}, entonces , Rango(A)= {#11} {#12} Rango(A^*)= {#13} {#14} nº de incognitas

SISTEMA {#15}

Sol: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»x«/mi»«mo»=«/mo»«/mrow»«/mstyle»«/math»{#16} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«mo»=«/mo»«/mstyle»«/math» {#17} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»z«/mi»«mo»=«/mo»«/mstyle»«/math»{#18}

Si m «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo»§#8800;«/mo»«/mstyle»«/math» {#19} y m «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo»§#8800;«/mo»«/mstyle»«/math» {#20} , entonces , Rango(A)= {#21} {#22} Rango(A^*)= {#23} {#24} nº de incognitas

SISTEMA {#25}

Sol: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»x«/mi»«mo»=«/mo»«/mrow»«/mstyle»«/math»{#26} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«mo»=«/mo»«/mstyle»«/math» {#27} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»z«/mi»«mo»=«/mo»«/mstyle»«/math»{#28}

]]> 28.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mi>x</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><reals/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>minimo</mi><mo>(</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>r</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>maximo</mi><mo>(</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>r</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>sol1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>sol2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d33</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><msub><mi>e3</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msub><mi>e3</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><msub><mi>e3</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d33</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_15_2 Discutir y resolver en función del parámetro m el siguiente sistema

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»-«/mo»«mn»3«/mn»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«mi»y«/mi»«mo»-«/mo»«mi»m«/mi»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Si m = {#1}, entonces , Rango(A)= {#2} {#3} Rango(A^*)= {#4} {#5} nº de incognitas

SISTEMA {#6}

Si m «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo»§#8800;«/mo»«/mstyle»«/math» {#10}, entonces , Rango(A)= {#11} {#12} Rango(A^*)= {#13} {#14} nº de incognitas

SISTEMA {#15}

]]> 18.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mi>x</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><reals/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>5</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_16 Antonio tiene un año más que Juan, y Luis, uno más que Ángel. Determina la edad de los cuatro sabiendo que la de Luis es la suma de la tercera parte más la séptima parte de la de Antonio y que la de Ángel es la suma de la cuarta parte más la quinta parte de la de Juan.

]]> 1.0000000 0.3333333 0 0 Edad-de-Antonio=#x1Edad-de-Angel=#y1 Edad-de-Juan=#z1Edad-de-Luis=#t1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>z</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>t</mi><mo>=</mo><mi>y</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>t</mi><mo>=</mo><mfenced><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>7</mn></mfrac></mrow></mfenced><mo>*</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mfenced><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mrow></mfenced><mo>*</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>A</mi><mi>n</mi><mi>t</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>E</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>A</mi><mi>n</mi><mi>g</mi><mi mathvariant="normal">e</mi><mi>l</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>E</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>J</mi><mi>u</mi><mi>a</mi><mi>n</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn><mspace linebreak="newline"/><mi>E</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>L</mi><mi>u</mi><mi mathvariant="normal">i</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>t</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_17 Por la compra de 8 kg de café natural y 5 kg de café torrefacto se han pagado 66 €. Hallar el precio del kilo de cada tipo de café, sabiendo que si se mezclan a partes iguales, el kilo sale a 5 €.

]]> 1.0000000 0.3333333 0 0 Precio-del-kilo-de-cafe-natural=#x1Precio-del-kilo-de-cafe-torrefacto=#y1 ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>66</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>16</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>14</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>l</mi><mo>-</mo><mi>k</mi><mi mathvariant="normal">i</mi><mi>l</mi><mi>o</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>c</mi><mi>a</mi><mi>f</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>n</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>a</mi><mi>l</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>P</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>l</mi><mo>-</mo><mi>k</mi><mi mathvariant="normal">i</mi><mi>l</mi><mi>o</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>c</mi><mi>a</mi><mi>f</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>t</mi><mi>o</mi><mi>r</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>f</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_18 Se dispone de tres cajas A, B y C con monedas de 1 euro. Se sabe que en total hay 36 euros. El número de monedas de A excede en dos a la suma de las monedas de las otras dos cajas. Si se traslada una moneda de la caja B a la caja A, esta tendrá el doble de monedas que B. Averigua cuántas monedas había en cada caja.

]]> 1.0000000 0.3333333 0 0 Monedas-en-la-caja-A=#x1Monedas-en-la-caja-B=#y1 Monedas-en-la-caja-C=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>36</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>=</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>+</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">e</mi><mi>n</mi><mo>-</mo><mi>l</mi><mi>a</mi><mo>-</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>a</mi><mo>-</mo><mi>A</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>M</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">e</mi><mi>n</mi><mo>-</mo><mi>l</mi><mi>a</mi><mo>-</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>a</mi><mo>-</mo><mi>B</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>M</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">e</mi><mi>n</mi><mo>-</mo><mi>l</mi><mi>a</mi><mo>-</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>a</mi><mo>-</mo><mi>C</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_19 Resolver el siguiente sistema lineal (utiliza el método que quieras):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mtable align=¨center¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mi»y«/mi»«mo»-«/mo»«mi»z«/mi»«mo»=«/mo»«mo»-«/mo»«mn»9«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»-«/mo»«mn»5«/mn»«mi»z«/mi»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 x= #x1y= #y1z=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>9</mn></mtd></mtr><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_2 Calcular el valor de m para que el siguiente sistema sea incompatible:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»8«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»10«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»+«/mo»«mi»m«/mi»«mi»z«/mi»«mo»=«/mo»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

m = {#1}

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mi>x</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_20_1 Discute el siguiente sistema:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»-«/mo»«mn»2«/mn»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»+«/mo»«mn»4«/mn»«mi»z«/mi»«mo»=«/mo»«mn»7«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»=«/mo»«mn»9«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Rango(A)= {#1} {#2} Rango(A^*)= {#3} {#4} nº de incognitas

SISTEMA {#5}

Solución: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«/mrow»«/mstyle»«/math»{#6} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«/mstyle»«/math» {#7} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«/mstyle»«/math»{#8}

]]> 8.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>7</mn></mtd></mtr><mtr><mtd><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>*</mo><mi>z</mi><mo>+</mo><mfrac><mn>8</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>8</mn><mn>3</mn></mfrac><mo>*</mo><mi>z</mi><mo>-</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">true</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_20_2 Discute y resuelve los siguientes sistemas:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»=«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«mi»y«/mi»«mo»=«/mo»«mn»11«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Rango(A)= {#1} {#2} Rango(A^*)= {#3} {#4} nº de incognitas

SISTEMA {#5}

]]> 5.0000000 0.3333333 0 <question><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_21 Resolver el siguiente sistema lineal (utiliza el método que quieras):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mtable align=¨center¨»«mtr»«mtd»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«mi»y«/mi»«mo»+«/mo»«mn»4«/mn»«mi»z«/mi»«mo»=«/mo»«mn»8«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mn»2«/mn»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»7«/mn»«mi»x«/mi»«mo»-«/mo»«mn»8«/mn»«mi»y«/mi»«mo»+«/mo»«mn»8«/mn»«mi»z«/mi»«mo»=«/mo»«mn»22«/mn»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 x= #x1y= #y1z=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>8</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>7</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>22</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_22 Juan y Pedro invierten 12000 euros cada uno. Juan coloca una cantidad A al 4% de interés (anual), una cantidad B al 5%, y el resto C al 6%, mientras que Pedro invierte la cantidad A al 5%, la B al 6%, y la C al 4%. Hallar las cantidades A, B y C, sabiendo que Juan obtiene unos intereses anuales de 630 euros, y Pedro obtiene 570 euros.

]]> 1.0000000 0.3333333 0 0 Cantidad-A=#x1Cantidad-B=#y1 Cantidad-C=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>12000</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo>.</mo><mn>04</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>06</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>630</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo>.</mo><mn>05</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>06</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>04</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>570</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3000.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3000.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6000.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi>A</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>C</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi>B</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>C</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>-</mo><mi>C</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_23 En la fabricación de cierta marca de chocolate se emplea leche, caco y almendras, siendo la proporción de leche doble que la de cacao y almendras juntas. Los precios por cada kilogramo de los ingredientes son: leche, 0,8 euros; cacao, 4 euros; almendras, 13 euros. En un día se fabrican 9000 kilos de ese chocolate, con un coste total de 25800 euros. ¿Cuántos kg se utilizan de cada ingrediente?.

]]> 1.0000000 0.3333333 0 0 Kilogramos-(litros)-de-leche=#x1Kilogramos-de-cacao=#y1 Kilogramos-de-almendras=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>9000</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mi>y</mi><mo>+</mo><mi>z</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mn>0</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>13</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>25800</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6000.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2000.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mi mathvariant="normal">i</mi><mi>log</mi><mi>r</mi><mi>a</mi><mi>m</mi><mi>o</mi><mi>s</mi><mo>-</mo><mo>(</mo><mi>l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>r</mi><mi>o</mi><mi>s</mi><mo>)</mo><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>l</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>K</mi><mi mathvariant="normal">i</mi><mi>log</mi><mi>r</mi><mi>a</mi><mi>m</mi><mi>o</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>c</mi><mi>a</mi><mi>c</mi><mi>a</mi><mi>o</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>K</mi><mi mathvariant="normal">i</mi><mi>log</mi><mi>r</mi><mi>a</mi><mi>m</mi><mi>o</mi><mi>s</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>a</mi><mi>l</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi>r</mi><mi>a</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_24 Una empresa dispone de 27200 € para actividades de formación de sus cien empleados. Después de estudiar las necesidades de los empleados, se ha decidido organizar tres cursos: A, B y C. el coste por persona para el curso A es de 400 €, para el curso B es de 160 €, y de 200 € para el C. Si la cantidad que se dedica al curso A es cinco veces mayor que la correspondiente al B, ¿cuántos empleados siguen cada curso?.

]]> 1.0000000 0.3333333 0 0 Nº-empleados-que-siguen-el-curso-A=#x1Nº-empleados-que-siguen-el-curso-B=#y1 Nº-empleados-que-siguen-el-curso-C=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>100</mn></mtd></mtr><mtr><mtd><mn>400</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>160</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>200</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>27200</mn></mtd></mtr><mtr><mtd><mn>400</mn><mo>*</mo><mi>x</mi><mo>=</mo><mn>5</mn><mo>*</mo><mn>160</mn><mo>*</mo><mi>y</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>º</mo><mo>-</mo><mi mathvariant="normal">e</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>o</mi><mi>s</mi><mo>-</mo><mi>q</mi><mi>u</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>g</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo>-</mo><mi mathvariant="normal">e</mi><mi>l</mi><mo>-</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>s</mi><mi>o</mi><mo>-</mo><mi>A</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>N</mi><mo>º</mo><mo>-</mo><mi mathvariant="normal">e</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>o</mi><mi>s</mi><mo>-</mo><mi>q</mi><mi>u</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>g</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo>-</mo><mi mathvariant="normal">e</mi><mi>l</mi><mo>-</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>s</mi><mi>o</mi><mo>-</mo><mi>B</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>N</mi><mo>º</mo><mo>-</mo><mi mathvariant="normal">e</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>o</mi><mi>s</mi><mo>-</mo><mi>q</mi><mi>u</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>g</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo>-</mo><mi mathvariant="normal">e</mi><mi>l</mi><mo>-</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>s</mi><mi>o</mi><mo>-</mo><mi>C</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_3 Calcular el valor de k para que el siguiente sistema sea incompatible:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»+«/mo»«mn»3«/mn»«mi»z«/mi»«mo»=«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»k«/mi»«mi»x«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

m {#1} {#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_4_11 Indica de los siguientes sistemas de ecuaciones cuales se pueden resolver por el método de Cramer.

a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»-«/mo»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mi»y«/mi»«mo»+«/mo»«mn»3«/mn»«mi»z«/mi»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»-«/mo»«mn»2«/mn»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»3«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»7«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»-«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»8«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»-«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

c) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math» d) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»-«/mo»«mn mathsize=¨14px¨»3«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mo mathsize=¨14px¨»-«/mo»«mn mathsize=¨14px¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 0.3333333 0 false true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> a)

]]> c)

]]> b)

]]> d)

]]> <question/> Ariketa_4_2_1 Resolver el siguiente sistema lineal (método de Cramer).

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 x= #x1y= #y1z=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_4_2_2 Resolver el siguiente sistema lineal (método de Cramer).

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»-«/mo»«mn mathsize=¨14px¨»3«/mn»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»+«/mo»«mn mathsize=¨14px¨»3«/mn»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mo mathsize=¨14px¨»-«/mo»«mn mathsize=¨14px¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathsize=¨14px¨»-«/mo»«mi mathsize=¨14px¨»x«/mi»«mo mathsize=¨14px¨»+«/mo»«mi mathsize=¨14px¨»y«/mi»«mo mathsize=¨14px¨»-«/mo»«mn mathsize=¨14px¨»2«/mn»«mi mathsize=¨14px¨»z«/mi»«mo mathsize=¨14px¨»=«/mo»«mn mathsize=¨14px¨»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 x= #x1y= #y1z=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_5 Dado el siguiente sistema:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»-«/mo»«mn»2«/mn»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»-«/mo»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Expresalo en forma matricial.
Sin resolverlo, indica de que tipo de sistema se trata.

(

{#1}

{#2}

{#3}

)

(

{#4}

)

(

{#5}

)

{#6}

{#7}

{#8}

{#9}

{#10}

{#11}

{#12}

{#13}

{#14}

{#15}

Es un sistema: {#16}

]]> 16.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a21</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a22</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a23</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a31</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a32</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a33</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b11</mi><mo>=</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b21</mi><mo>=</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b31</mi><mo>=</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c11</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c21</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c31</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_6 Discutir en función del parámetro m el siguiente sistema

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mi»m«/mi»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»=«/mo»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«mi»y«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Si m = {#1}, entonces , Rango(A)= {#2} {#3} Rango(A^*)= {#4} {#5} nº de incognitas

SISTEMA {#6}

Si m «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo»§#8800;«/mo»«/mstyle»«/math» {#7}, entonces , Rango(A)= {#8} {#9} Rango(A^*)= {#10} {#11} nº de incognitas

SISTEMA {#12}

]]> 12.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><reals/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_7 Discutir y resolver en función del parámetro m el siguiente sistema

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«mo»-«/mo»«mi»m«/mi»«mi»y«/mi»«mo»-«/mo»«mn»3«/mn»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»y«/mi»«mo»-«/mo»«mi»z«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

Si m = {#1}, entonces , Rango(A)= {#2} {#3} Rango(A^*)= {#4} {#5} nº de incognitas

SISTEMA {#6}

SISTEMA {#15}

]]> 18.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mi>x</mi></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><reals/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>e</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi><mo>=</mo><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>e1</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>19</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>19</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ariketa_8 Una cooperativa farmacéutica reparte los productos en tres frascos distintos: A, B y C. Los frascos de tipo A pesan 250 gramos y cuestan 6 €; los de tipo B pesan 500 gramos y cuestan 10,8 €; y los de tipo C pesan un kilogramo y cuestan 19,8 €. En cierta farmacia se ha dejado un lote de cinco frascos que pesa 2,5 kilogramos y cuesta 53,4 €. ¿ Cuántos frascos de cada tipo ha comprado dicha farmacia?.

]]> 1.0000000 0.3333333 0 0 Frascos-de-tipoA=#x1Frascos-de-tipoB=#y1 Frascos-de-tipoC=#z1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>5</mn></mtd></mtr><mtr><mtd><mn>250</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>500</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>1000</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>2500</mn></mtd></mtr><mtr><mtd><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>19</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>53</mn><mo>.</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>r</mi><mi>a</mi><mi>s</mi><mi>cos</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>t</mi><mi mathvariant="normal">i</mi><mi>p</mi><mi>o</mi><mi>A</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>F</mi><mi>r</mi><mi>a</mi><mi>s</mi><mi>cos</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>t</mi><mi mathvariant="normal">i</mi><mi>p</mi><mi>o</mi><mi>B</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mo> </mo><mspace linebreak="newline"/><mi>F</mi><mi>r</mi><mi>a</mi><mi>s</mi><mi>cos</mi><mo>-</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo>-</mo><mi>t</mi><mi mathvariant="normal">i</mi><mi>p</mi><mi>o</mi><mi>C</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>