1rBTX 03. EQUACIONS I INEQUACIONS/1.3.3 Sistemes 1.3.3.10DT REDUCCIÓ
Reducció

En el sistema lineal «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»4«/mn»«mi mathvariant=¨bold-italic¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»10«/mn»«mi mathvariant=¨bold-italic¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»6«/mn»«mi mathvariant=¨bold-italic¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold-italic¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»19«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

Elimino x: calculo el mcm de 4 i -6 = 12 i igualo els coeficients,

multiplicant la 1a per 3(12:4) i la 2a per -2(12:-6)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»12«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»30«/mn»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»18«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»12«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»10«/mn»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»38«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«/math»

REST0 la 2a de la 1a i ens queda: -20y = -20, o sigui y = 1.

Elimino la y per trobar la x, o substitueixo.

Solució: (4,1) 
]]> 0.0000000 0.0000000 0 1.3.3.11Q Reducció CD Del sistema d'equacions següent:«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«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) Determina el mcm dels coeficients de la x

b) Troba la solució del sistema. 

  Format de la resposta: {-2,3/2} simplificada!

 

]]> 1.0000000 0.3333333 0 0 a. mcm=#sol1b. Solució=#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"><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>A2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd><mtd><mi>a1</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd><mtd><mi>a2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>w3</mi><mo>=</mo><mi>mcd</mi><mo>(</mo><mi>a11</mi><mo>,</mo><mi>a21</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>w4</mi><mo>=</mo><mi>mcd</mi><mo>(</mo><mi>a12</mi><mo>,</mo><mi>a22</mi><mo>)</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>rang</mi><mo>(</mo><mi>A1</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></mfenced><mo>∧</mo><mo>(</mo><mfenced close="|" open="|"><mi>a11</mi></mfenced><mo>&lt;</mo><mfenced close="|" open="|"><mi>a21</mi></mfenced><mo>)</mo><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>a12</mi></mfenced><mo>&lt;</mo><mfenced close="|" open="|"><mi>a22</mi></mfenced></mrow></mfenced><mo>∧</mo><mo>(</mo><mi>w3</mi><mo>≠</mo><mn>1</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>w4</mi><mo>≠</mo><mn>1</mn><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a2</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced></mfrac></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a1</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a2</mi></mtd></mtr></mtable></mfenced><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced></mfrac></mtd></mtr></mtable></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>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>a1</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>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>w1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a11</mi><mo>,</mo><mi>a21</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a12</mi><mo>,</mo><mi>a22</mi><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mi>w1</mi><mfenced close="|" open="|"><mi>a11</mi></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mfenced close="|" open="|"><mi>a11</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfrac><mi>w1</mi><mfenced close="|" open="|"><mi>a21</mi></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m21</mi><mo>=</mo><mfenced close="|" open="|"><mi>a21</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>e1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e22</mi><mo>=</mo><mi>f2</mi><mo>*</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>a11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>f2</mi><mo>*</mo><mi>a21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a11</mi><mo>*</mo><mi>a21</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>z1</mi><mo>=</mo><mo>&quot;</mo><mi>igual</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z2</mi><mo>=</mo><mo>&quot;</mo><mi>restem</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mn>2</mn><mi>a</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mn>1</mn><mi>a</mi><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>z1</mi><mo>=</mo><mo>&quot;</mo><mi>diferent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z2</mi><mo>=</mo><mo>&quot;</mo><mi>les</mi><mo>&nbsp;</mo><mi>sumem</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></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"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mfrac><mi>w2</mi><mfenced close="|" open="|"><mi>a12</mi></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m12</mi><mo>=</mo><mfenced close="|" open="|"><mi>a12</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mfrac><mi>w2</mi><mfenced close="|" open="|"><mi>a22</mi></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m22</mi><mo>=</mo><mfenced close="|" open="|"><mi>a22</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e31</mi><mo>=</mo><mi>g1</mi><mo>*</mo><mi>e1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e32</mi><mo>=</mo><mi>g2</mi><mo>*</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>g1</mi><mo>*</mo><mi>a12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>g2</mi><mo>*</mo><mi>a22</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a12</mi><mo>*</mo><mi>a22</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>v1</mi><mo>=</mo><mo>&quot;</mo><mi>igual</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mo>&quot;</mo><mi>restem</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mn>2</mn><mi>a</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mn>1</mn><mi>a</mi><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>v1</mi><mo>=</mo><mo>&quot;</mo><mi>diferent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mo>&quot;</mo><mi>les</mi><mo>&nbsp;</mo><mi>sumem</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a11</mi><mo>,</mo><mi>a21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s1</mi><mo>,</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></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"><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>19</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>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</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"><mo>(</mo><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>,</mo><mn>16</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f1</mi><mo>,</mo><mi>f2</mi><mo>,</mo><mi>g1</mi><mo>,</mo><mi>g2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>36</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>171</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>80</mn><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>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><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>&#xA0;</mo><mi>m</mi><mi>c</mi><mi>m</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mi>S</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#xF3;</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_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> Per eliminar x, el mcm de #a11 i #a21 és #w1.

Així doncs, multipliquem

  • la 1a per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8594;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»21«/mn»«/math»
  • la 2a per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8594;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»22«/mn»«/math»

i com que #b1 i #b2 tenen signe #z1,  #z2 per eliminar x.

 

]]> Per eliminar y, el mcm de #a12 i #a22 és #w2.

Així doncs, multipliquem

  • la 1a per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»g«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8594;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»31«/mn»«/math»
  • la 2a per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»22«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»g«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8594;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»32«/mn»«/math»

i com que #c1 i #c2 tenen signe #v1,  #v2 per eliminar y.

 

]]> 1.3.3.15Q ReduccióAleatori Determina les solucions de: «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»


Format de la resposta: Si el sistema és 

  • compatible determinat: escriu la solució: {-21,11/15}
  • compatible indeterminat: escriu 1
  • incompatible, escriu 2
]]> 1.0000000 0.3333333 0 0 #sol <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>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>A2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd><mtd><mi>a1</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd><mtd><mi>a2</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mrow><mfenced><mrow><mi>rang</mi><mo>(</mo><mi>A1</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></mfenced><mo>∧</mo><mo>(</mo><mi>a11</mi><mo>&lt;</mo><mi>a21</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a2</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced></mfrac></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a1</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a2</mi></mtd></mtr></mtable></mfenced><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced></mfrac></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s1</mi><mo>,</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>a11</mi></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>a11</mi></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd/></mtr></mtable></apply></apply></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>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>a1</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>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a11</mi><mo>,</mo><mi>a21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mi>w1</mi><mfenced close="|" open="|"><mi>a11</mi></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfrac><mi>w1</mi><mfenced close="|" open="|"><mi>a21</mi></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>e1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e22</mi><mo>=</mo><mi>f2</mi><mo>*</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>a11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>f2</mi><mo>*</mo><mi>a21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a11</mi><mo>*</mo><mi>a21</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>z1</mi><mo>=</mo><mo>&quot;</mo><mi>igual</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z2</mi><mo>=</mo><mo>&quot;</mo><mi>restem</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mn>2</mn><mi>a</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mn>1</mn><mi>a</mi><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>z1</mi><mo>=</mo><mo>&quot;</mo><mi>diferent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z2</mi><mo>=</mo><mo>&quot;</mo><mi>les</mi><mo>&nbsp;</mo><mi>sumem</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></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><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>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>0</mn></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"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f1</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</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>10</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>0</mn></math></output></command><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>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per eliminar x, el mcm de #a11 i #a21 és #w1.

Així doncs, multipliquem

  • la 1a per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8594;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»21«/mn»«/math»
  • la 2a per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8594;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»22«/mn»«/math»

i com que #b1 i #b2 tenen signe #z1,  #z2 per eliminar x.

 

]]> Si trobem solució, el sistema és compatible determinat.

Si surt 0x+0y=0, el sistema és compatible indeterminat.

Si surt 0x+0y=No-zero el sistema és incompatible.

]]> 1.3.3.16Q Tipus de sistema Considera el sistema d'equacions«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¨»01«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e_«/mi»«mn mathvariant=¨bold¨»02«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
Quin tipus de sistema és? Quines solucions té?

Atenció: hi ha més d'una resposta vàlida

]]> 1.0000000 1.0000000 0 false true abc #r_11 #r_12 #r_21 #r_22 #r_31 #r_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;maction actiontype=&quot;comment&quot;&gt;&lt;comment&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;Sistema&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;CD&lt;/mi&gt;&lt;/math&gt;&lt;/comment&gt;&lt;/maction&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_11&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_12&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_13&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_21&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_22&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_23&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;rang&lt;/mi&gt;&lt;mfenced&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_11&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;a_12&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_21&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;a_22&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_11&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_11&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_12&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_13&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_12&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_21&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_22&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_23&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;maction actiontype=&quot;comment&quot;&gt;&lt;comment&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;Regla&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;de&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;Cramer&lt;/mi&gt;&lt;/math&gt;&lt;/comment&gt;&lt;/maction&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_11&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;a_22&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_21&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;a_12&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D_x&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_13&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;a_22&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_23&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;a_12&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D_y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_11&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;a_23&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_21&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;a_13&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;D_x&lt;/mi&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;D_y&lt;/mi&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;maction actiontype=&quot;comment&quot;&gt;&lt;comment&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;Sistema&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mi&gt;IND&lt;/mi&gt;&lt;/math&gt;&lt;/comment&gt;&lt;/maction&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_11&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_12&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_13&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_21&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;b_11&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_22&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;b_12&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_23&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;b_13&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_21&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b_11&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b_12&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b_13&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_22&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b_21&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b_22&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b_23&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;maction actiontype=&quot;comment&quot;&gt;&lt;comment&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;Sistema&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;INCOMPATIBLE&lt;/mi&gt;&lt;/math&gt;&lt;/comment&gt;&lt;/maction&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_11&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_12&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_13&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_21&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;k_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;c_11&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_22&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;k_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;c_12&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_23&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;c_23&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mi&gt;k_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;c_13&lt;/mi&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_31&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;c_11&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c_12&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;c_13&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;c_21&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c_22&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;c_23&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_01&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;e_11&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;e_21&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;e_31&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;if&lt;/csymbol&gt;&lt;mrow&gt;&lt;mi&gt;e_01&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;e_11&lt;/mi&gt;&lt;/mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;e_02&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;e_12&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_11&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;compatible&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;determinat&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_21&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;incompatible&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_22&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;Moltes&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;solucions&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_31&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;compatible&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;indeterminat&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;Cap&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;solució&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_12&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfenced close=&quot;]&quot; open=&quot;[&quot;&gt;&lt;mrow&gt;&lt;mi&gt;s_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s_2&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;if&lt;/csymbol&gt;&lt;mrow&gt;&lt;mi&gt;e_01&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;e_21&lt;/mi&gt;&lt;/mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;e_02&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;e_22&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_31&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;compatible&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;determinat&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_21&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;incompatible&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_12&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;Moltes&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;solucions&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_11&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;compatible&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;indeterminat&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;Cap&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;solució&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_22&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mfenced close=&quot;]&quot; open=&quot;[&quot;&gt;&lt;mrow&gt;&lt;mi&gt;s_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s_2&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;e_02&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;e_32&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_21&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;compatible&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;determinat&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_11&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;incompatible&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_22&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;Moltes&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;solucions&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_31&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;és&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;compatible&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;indeterminat&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_12&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;mi&gt;Cap&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;solució&lt;/mi&gt;&lt;mo&gt;&amp;quot;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;r_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfenced close=&quot;]&quot; open=&quot;[&quot;&gt;&lt;mrow&gt;&lt;mi&gt;s_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s_2&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/apply&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_01&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_12&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;14&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_22&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;95&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;45&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;60&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;14&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e_02&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;95&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;45&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;60&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_11&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;ms&gt;és&lt;/ms&gt;&lt;mo&gt; &lt;/mo&gt;&lt;ms&gt;compatible&lt;/ms&gt;&lt;mo&gt; &lt;/mo&gt;&lt;ms&gt;indeterminat&lt;/ms&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_12&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;ms&gt;Moltes&lt;/ms&gt;&lt;mo&gt; &lt;/mo&gt;&lt;ms&gt;solucions&lt;/ms&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_21&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;ms&gt;és&lt;/ms&gt;&lt;mo&gt; &lt;/mo&gt;&lt;ms&gt;incompatible&lt;/ms&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_22&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfenced close=&quot;]&quot; open=&quot;[&quot;&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mn&gt;106&lt;/mn&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;76&lt;/mn&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_31&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;ms&gt;és&lt;/ms&gt;&lt;mo&gt; &lt;/mo&gt;&lt;ms&gt;compatible&lt;/ms&gt;&lt;mo&gt; &lt;/mo&gt;&lt;ms&gt;determinat&lt;/ms&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;ms&gt;Cap&lt;/ms&gt;&lt;mo&gt; &lt;/mo&gt;&lt;ms&gt;solució&lt;/ms&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession></question> 1.3.3.20DT IGUALACIÓ
Igualació

Si les equacions són del tipus: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Igualem: 5x - 4 = 2x + 5 i resolem: x = 3.
Si substituïm x per 3  en qualsevol de les dues, y = 11.

Solució: (3,11) 
]]> 0.0000000 0.0000000 0 1.3.3.21Q Igualació y=mx+n Calculeu per igualació, les solucions del sistema: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«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»

Forma de la resposta:  enter o fracció SIMPLIFICADA 





]]> 1.0000000 0.5000000 0 0 x=#s1y=#s2]]> <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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>m_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>e_1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n_1</mi></mtd></mtr><mtr><mtd><mi>e_2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n_2</mi></mtd></mtr><mtr><mtd><mi>f_1</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n_1</mi></mtd></mtr><mtr><mtd><mi>f_2</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n_2</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>m_1</mi><mo>≠</mo><mi>m_2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_1</mi><mo>≠</mo><mi>n_2</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n_1</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n_2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</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><mo>-</mo><mn>10</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>66</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>66</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>x</mi><mo>=</mo><mo>#</mo><mi>s</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>s</mi><mn>2</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="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50 50</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> N'hi ha prou amb escriure:

#f_1 = #f_2
i aïllar la x.
Un cop s'ha trobat la x, es substitueix en qualsevol de les dues equacions per determinar el valor de y.
NO SIMPLIFICAR LA FRACCIÓ ES COMPTA COM INCORRECTE.
]]> 1.3.3.22Q Igualació x=vt+a Calculeu per igualació, les solucions del 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»

Forma de la resposta:  enter o fracció SIMPLIFICADA 





]]> 1.0000000 0.5000000 0 0 x=#x1t=#t1]]> <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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>m_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</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>e_1</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>n_1</mi></mtd></mtr><mtr><mtd><mi>e_2</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>n_2</mi></mtd></mtr><mtr><mtd><mi>f_1</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>n_1</mi></mtd></mtr><mtr><mtd><mi>f_2</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>n_2</mi></mtd></mtr><mtr><mtd><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>n_1</mi></mtd></mtr><mtr><mtd><mi>x</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>n_2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>x1</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable><mrow><mfenced><mrow><mi>m_1</mi><mo>≠</mo><mi>m_2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_1</mi><mo>≠</mo><mi>n_2</mi></mrow></mfenced></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>5</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>4</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>t</mi><mo>=</mo><mo>-</mo><mfrac><mn>5</mn><mn>8</mn></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mfrac><mn>57</mn><mn>8</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>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></math></output></command><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>57</mn><mn>8</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>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>t</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^(-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="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50 50</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> N'hi ha prou amb escriure:

#f_1 = #f_2
i aïllar la t.
Un cop s'ha trobat la t, es substitueix en qualsevol de les dues equacions per determinar el valor de x.
NO SIMPLIFICAR LA FRACCIÓ ES COMPTA COM INCORRECTE.
]]> 1.3.3.30DT SUBSTITUCIÓ
Substitució

Si un dels coeficients és 1: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»7«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
aïllem x en la primera equació: x = 5y + 9
el substituïm en la segona: 3(5y+9) + 2y = -7
resolem: 17y + 27 = - 7 <=> y = -2
i substituint y per -2 en qualsevol de les dues: x = -1.

Solució: (-1,-2)
]]> 0.0000000 0.0000000 0 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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&#xA0;</mo><mi>A</mi><mi>&#xEF;</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>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>w</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</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>&#xA0;</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
]]> 1.3.3.50DT SISTEMES NO LINEALS Resolució de sistemes no lineals Un sistema no lineal es resol per substitució.
Exemple:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»20«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
Aïllo y en la primera equació: y = 6 - x
Substitueixo en la segona equació: x2 + (6-x)2 = 20 i resolc el 2n grau: 2x2 - 12x + 16 = 0.
Solucions: (2,4) i (4,2) ]]> 0.0000000 0.0000000 0 1.3.3.51Q NoLineal Suma i quadrat Resol el sistema d'equacions següent:

#e_1

Format de la resposta: {{1,2},{3,4}} 

 
]]> 1.0000000 0.5000000 0 0 #sol <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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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>a</mi><mo>&lt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mi>s_1</mi></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>s_2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mi>s_1</mi><mo>-</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>,</mo><mi>b</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>b</mi><mo>,</mo><mi>a</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</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>s_2</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>sol</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><mo>-</mo><mn>4</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal aïllar x en la primera: y = #w_1
i substituir en la segona: x2 + (#w_1)2 = #s_2.
Penseu en emprar la fórmula (a - b)2 = a2 -2ab + b2 per calcular (#w_1)2

]]> 1.3.3.52Q NoLineal Diferència i quadrat Resol el sistema d'equacions següent:

#e_1

Format de la resposta: {{1,2},{3,4}} 

 
]]> 1.0000000 0.5000000 0 0 #sol <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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mi>s_1</mi></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>s_2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>s_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>s_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><msup><mfenced><mi>s_1</mi></mfenced><mn>2</mn></msup><mo>-</mo><mi>s_2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>s_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><msup><mfenced><mi>s_1</mi></mfenced><mn>2</mn></msup><mo>-</mo><mi>s_2</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</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>r_12</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>2</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r_11</mi><mo>&lt;</mo><mi>r_12</mi></mrow><mtable><mtr><mtd><mi>t_11</mi><mo>=</mo><mi>r_11</mi></mtd></mtr><mtr><mtd><mi>t_12</mi><mo>=</mo><mi>r_12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>t_11</mi><mo>=</mo><mi>r_12</mi></mtd></mtr><mtr><mtd><mi>t_12</mi><mo>=</mo><mi>r_11</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_11</mi><mo>=</mo><mi>t_11</mi><mo>-</mo><mi>s_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_12</mi><mo>=</mo><mi>t_12</mi><mo>-</mo><mi>s_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t_11</mi><mo>,</mo><mi>u_11</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t_12</mi><mo>,</mo><mi>u_12</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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>a</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</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>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn></math></output></command><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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>4</mn><mo>,</mo><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn><mo>,</mo><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal aïllar x en la primera: y = #w_1
i substituir en la segona: x2 + (#w_1)2 = #s_2.
Penseu en emprar la fórmula (a - b)2 = a2 -2ab + b2 per calcular (#w_1)2

]]> 1.3.3.53Q NoLineal Diferència i producte Resol el sistema d'equacions següent:

#e_1

Format de la resposta: {{1,2},{3,4}} 

 
]]> 1.0000000 0.5000000 0 0 #sol <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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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><mfenced><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mi>s_1</mi></mtd></mtr><mtr><mtd><mi>x</mi><mo>·</mo><mi>y</mi><mo>=</mo><mi>s_2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>s_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mi>x</mi><mo>*</mo><mi>w_1</mi><mo>-</mo><mi>s_2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>x</mi><mo>*</mo><mi>w_1</mi><mo>=</mo><mi>s_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</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>r_12</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>2</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r_11</mi><mo>&lt;</mo><mi>r_12</mi></mrow><mtable><mtr><mtd><mi>t_11</mi><mo>=</mo><mi>r_11</mi></mtd></mtr><mtr><mtd><mi>t_12</mi><mo>=</mo><mi>r_12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>t_11</mi><mo>=</mo><mi>r_12</mi></mtd></mtr><mtr><mtd><mi>t_12</mi><mo>=</mo><mi>r_11</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_11</mi><mo>=</mo><mi>t_11</mi><mo>-</mo><mi>s_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_12</mi><mo>=</mo><mi>t_12</mi><mo>-</mo><mi>s_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>t_11</mi><mo>,</mo><mi>u_11</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>t_12</mi><mo>,</mo><mi>u_12</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t_11</mi><mo>,</mo><mi>u_11</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t_12</mi><mo>,</mo><mi>u_12</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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>a</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</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>s_2</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>sol</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><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal aïllar x en la primera: y = #w_1
i substituir en la segona: x · (#w_1) = #s_2,
i trobem les solucions de l'equació. 

]]> 1.3.3.54Q SistNoLineal x^2+y^2, x^2-y^2 Resol el sistema d'equacions següent:   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»

Es recomana sumar les equacions

Format: {[-2,3],[-2,7],[1,-3],[1,1]}

]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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>a</mi><mo>&lt;</mo><mi>b</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>t_1</mi><mo>=</mo><mo>-</mo><mfenced><msqrt><mfrac><mrow><mi>s_1</mi><mo>+</mo><mi>s_2</mi></mrow><mn>2</mn></mfrac></msqrt></mfenced></mtd></mtr><mtr><mtd><mi>t_2</mi><mo>=</mo><mfenced><msqrt><mfrac><mrow><mi>s_1</mi><mo>+</mo><mi>s_2</mi></mrow><mn>2</mn></mfrac></msqrt></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>t_1</mi><mo>&lt;</mo><mi>t_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>s_1</mi></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>s_2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>s_1</mi><mo>+</mo><mi>s_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mi>s_1</mi><mo>+</mo><mi>s_2</mi></math></input></command><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><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>s_1</mi></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>s_2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_11</mi><mo>=</mo><mo>-</mo><msqrt><mrow><mi>s_1</mi><mo>-</mo><msup><mfenced><mi>t_1</mi></mfenced><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_12</mi><mo>=</mo><msqrt><mrow><mi>s_1</mi><mo>-</mo><msup><mfenced><mi>t_1</mi></mfenced><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_21</mi><mo>=</mo><mo>-</mo><msqrt><mrow><mi>s_1</mi><mo>-</mo><msup><mfenced><mi>t_2</mi></mfenced><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u_22</mi><mo>=</mo><msqrt><mrow><mi>s_1</mi><mo>-</mo><msup><mfenced><mi>t_2</mi></mfenced><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>t_1</mi><mo>,</mo><mi>u_11</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>t_1</mi><mo>,</mo><mi>u_12</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>t_2</mi><mo>,</mo><mi>u_21</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>t_2</mi><mo>,</mo><mi>u_22</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mo>-</mo><mn>8</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</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"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></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"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></mfenced></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"><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></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"><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></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>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sumant les equacions es troba: 2x2 = #w_1
i x correspon a les dues arrels de #w_1 (positiva i negativa).
Després cal substituir x2 en qualsevol de les dues equacions per trobar y2 i, per tant, els dos valors possible de y per cada valor de x.

]]>