1rBTX 03. EQUACIONS I INEQUACIONS/1.3.3 Sistemes 1.3.3.31Q Substitució 2x2 CD Amb el sistema: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

a) Aïlla la variable més fàcil d'aïllar (Format: x=y+2)

b) Calcula el valor de x en la solució

c) Calcula el valor de y en la solució

Format de x i y: nombre enter o fracció SIMPLIFICADA

]]> 1.0000000 0.5000000 0 0 a. Aïllament: =#w1b. x=#sol1c. y=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Aïllar</mi><mo> </mo><mi>x</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>p11</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>p12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>p21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>p22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>q2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mi>p11</mi><mo>*</mo><mi>p22</mi><mo>-</mo><mi>p12</mi><mo>*</mo><mi>p21</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Aïllar</mi><mo> </mo><mi>y</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>m12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>m21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>m22</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mi>m11</mi><mo>*</mo><mi>m22</mi><mo>-</mo><mi>m12</mi><mo>*</mo><mi>m21</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Creació</mi><mo> </mo><mi>sistema</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>a11</mi><mo>=</mo><mi>p11</mi></mtd></mtr><mtr><mtd><mi>a12</mi><mo>=</mo><mi>p12</mi></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>p21</mi></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>p22</mi></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>q1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>q2</mi></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>q1</mi><mo>-</mo><mi>p12</mi><mo>*</mo><mi>y</mi></mtd></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mi>y</mi></mtd></mtr><mtr><mtd><mi>w11</mi><mo>=</mo><mi>q1</mi><mo>-</mo><mi>p12</mi><mo>*</mo><mi>y</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>a11</mi><mo>=</mo><mi>m11</mi></mtd></mtr><mtr><mtd><mi>a12</mi><mo>=</mo><mi>m12</mi></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>m21</mi></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>m22</mi></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>n1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>n2</mi></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mi>y</mi></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>n2</mi><mo>-</mo><mi>m21</mi><mo>*</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>w11</mi><mo>=</mo><mi>n2</mi><mo>-</mo><mi>m21</mi><mo>*</mo><mi>x</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>a11</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a12</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a21</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a22</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b2</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Resolució</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a11</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a12</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>a21</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a22</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>x</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>y</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>a11</mi><mo>,</mo><mi>a22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>13</mn><mn>9</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>7</mn><mn>9</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>13</mn><mn>9</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>7</mn><mn>9</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo> </mo><mi>A</mi><mi>ï</mi><mi>l</mi><mi>l</mi><mi>a</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>:</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>w</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo> </mo><mi>x</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mi>y</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></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> Com que el coeficient de #w és 1 en la primera equació, aïllem #w: #w1

i substituïm #w per #w11 en l'altra equació per trobar #w2

UNA FRACCIÓ NO SIMPLIFICADA ÉS INCORRECTA

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