1MA 05. RECTES EN EL PLA/1MA.05.3 PosRelativa Intersecció/1MA.05.3.2 Intersecció2Rectes 1MA.05.3.2.33Q Intersecció ParaCart Substitució Resolent el sistema per substitució, determina en quin punt es tallen les dues rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»?
Format de la resposta:

a) Valor de k=-2/3 (simplificat)

b) Punt =(2/3,-1/3) simplificat i entre parèntesis.

]]> Les rectes es tallen en el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»per«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#7F0000¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»1«/mn»«/mstyle»«/math»

#G1

]]> 1.0000000 0.5000000 0 0 a) k=#sol1b) Punt =#sol2]]> <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 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xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>546</mn><mn>41</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>939</mn><mn>41</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>a</mi><mo>)</mo><mo> </mo><mi>k</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> </mo><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></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"/><data name="inputCompound">true</data></localData></question> Amb les equacions paramètriques de r:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

substitueix x i y en l'equació de s, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/mstyle»«/math», per trobar el valor de k = #k1

Substitueix k per aquest valor en les equacions paramètriques de r, i trobaràs les coordenades del punt

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