document.write( "Question 174554: 7X + 3Y = 14 , 5X + 9Y = 10\r
\n" ); document.write( "\n" ); document.write( " 4X + Y = 16 , 2X + 3Y = 24\r
\n" ); document.write( "\n" ); document.write( " 12X + Y = 25 , 8X - 2Y = 14\r
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Algebra.Com's Answer #129584 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"system%28+7X+%2B+3Y+=+14+%2C++%0D%0A5X+%2B+9Y+=+10%29\"$
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document.write( "Notice the 3Y in the first equation and the 9Y\r\n" );
document.write( "in the second equation.  If you multiply the\r\n" );
document.write( "first equation by -3, the 3Y will become -9Y and\r\n" );
document.write( "then if you add the two equations, the Y's will\r\n" );
document.write( "cancel.  So let's multiply the first equation by\r\n" );
document.write( "-3:\r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "Now we add corresponding terms.\r\n" );
document.write( "-21X added to 5X gives -16X,\r\n" );
document.write( "-9Y added to 9Y gives 0,\r\n" );
document.write( "-42 added to 10 gives -32, so\r\n" );
document.write( "by adding vertically term by \r\n" );
document.write( "term we have the equation:\r\n" );
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document.write( "Divide both sides by -16:\r\n" );
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document.write( "Now pick either one of the original\r\n" );
document.write( "equations and substitute 2 for X:\r\n" );
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document.write( "-----\r\n" );
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document.write( "Notice the 4X in the first equation and the 2X\r\n" );
document.write( "in the second equation.  If you multiply the\r\n" );
document.write( "second equation by -2, the 2X will become -4X and\r\n" );
document.write( "then if you add the two equations, the X's will\r\n" );
document.write( "cancel.  So let's multiply the second equation by\r\n" );
document.write( "-2:\r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "Now we add corresponding terms.\r\n" );
document.write( "4X added to -4X gives 0,\r\n" );
document.write( "Y added to -6Y gives -5Y,\r\n" );
document.write( "16 added to -48 gives -32, so\r\n" );
document.write( "by adding vertically term by \r\n" );
document.write( "term we have the equation:\r\n" );
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document.write( "Divide both sides by -5:\r\n" );
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document.write( "We could substitute this fraction in\r\n" );
document.write( "for Y as we did in the previous problem.\r\n" );
document.write( "However, unlike the previous problem,\r\n" );
document.write( " is difficult to subtitute.\r\n" );
document.write( "So instead we will start over:\r\n" );
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document.write( "and this time we'll eliminate Y:\r\n" );
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document.write( "Notice the Y in the first equation and the 3Y\r\n" );
document.write( "in the second equation.  If you multiply the\r\n" );
document.write( "first equation by -3, the Y will become -3Y and\r\n" );
document.write( "then if you add the two equations, the Y's will\r\n" );
document.write( "cancel.  So let's multiply the first equation by\r\n" );
document.write( "-3:\r\n" );
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document.write( "\r\n" );
document.write( "Simplifying:\r\n" );
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document.write( "Now we add corresponding terms.\r\n" );
document.write( "-12X added to 2X gives -10X,\r\n" );
document.write( "-3Y added to 3Y gives 0,\r\n" );
document.write( "-48 added to 24 gives -24, so\r\n" );
document.write( "by adding vertically term by \r\n" );
document.write( "term we have the equation:\r\n" );
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document.write( "Divide both sides by -16:\r\n" );
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document.write( "---\r\n" );
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document.write( "You do this one by yourself.  It's just like the first one.\r\n" );
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document.write( "Answer: , \r\n" );
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document.write( "Edwin

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