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 <question type="category"><category><text>1MA 05. RECTES EN EL PLA/1MA.05.3 PosRelativa Intersecció/1MA.05.3.2 Intersecció2Rectes</text></category></question>
 
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      <text>1MA.05.3.2.30DT PINTERSECCIÓ SUBSTITUCIÓ</text>
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<td style="background-color: #003300;" align="center" valign="middle"><span style="color: #ffff99; font-size: large;" data-mce-mark="1">Punt d'intersecció: substitució</span></td>
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<p style="text-align: justify;"><strong style="color: #003300;"><span style="font-size: small;">Si tenim les equacions paramètriques (o la contínua o la vectorial) podem emprar el mètode de substitució </span></strong><span style="color: #003300;"><strong style="color: #003300;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»</strong></span></p>
<p style="text-align: justify;"><span style="color: #003300;"> </span></p>
<p style="text-align: justify;"><span style="color: #003300;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»Substituint«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»per«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»les«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»equacions«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»param§#232;triques«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»:«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»4«/mn»«/math»</span></p>
<p style="text-align: justify;"><span style="font-size: small;" data-mce-mark="1"><strong style="color: #000080; line-height: 1.4;"><span style="font-size: small;" data-mce-mark="1"><span style="font-size: small;" data-mce-mark="1"><span style="color: #003300;">Substituïm la k en les equacions paramètriques, </span><span style="font-size: small;" data-mce-mark="1"><span style="color: #003300;"> i trobem el punt d'intersecció (-1,2).</span> </span></span></span></strong></span></p>
<p style="text-align: center;"><span style="font-size: medium; color: #008000;"><strong style="line-height: 1.4;">Si dona 0k=0, són coincidents. </strong></span></p>
<p style="text-align: center;"><span style="font-size: medium; color: #008000;"><strong style="line-height: 1.4;">Si dona 0k≠0, són paral·leles.</strong></span></p>
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