document.write( "Question 1134370: 3x-y-2z= 18
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Algebra.Com's Answer #751740 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
\"system%283x-y-2z=+18%2C%0D%0A2x%2By-2z=15%2C%0D%0Ax%2B3y-z=10%29\"
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document.write( "Pick a pair of equations and a letter to eliminate.\r\n" );
document.write( "[Note: There are 6 different ways to start, all correct!]\r\n" );
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document.write( "I will pick the first two equations and y to eliminate,\r\n" );
document.write( "because it happens to be the easiest because all you have to\r\n" );
document.write( "do is add them and y will be eliminated:\r\n" );
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document.write( "\"system%283x-y-2z=+18%2C%0D%0A2x%2By-2z=15%29\"\r\n" );
document.write( "\"matrix%281%2C5%2C++++%22%22%2C5x%2C%22%22%2C%22%22%2C-4z=33%29\" \r\n" );
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document.write( "Now pick a different pair of equations and eliminate the\r\n" );
document.write( "SAME letter eliminated first. \r\n" );
document.write( "[Note: we have to pick one of the same equations again, but\r\n" );
document.write( "we must pick the third equation this time.]\r\n" );
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document.write( "So I will pick the first and third equations and y to eliminate:\r\n" );
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document.write( "\"system%283x-y-2z=+18%2C%0D%0Ax%2B3y-z=10%29\"\r\n" );
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document.write( "To eliminate y we multiply the first equation through by 3\r\n" );
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document.write( "\"system%289x-3y-6z=+54%2C%0D%0A%22%22x%2B3y-z=10%29\"\r\n" );
document.write( "\"matrix%281%2C5%2C++++%22%22%2C10x%2C%22%22%2C%22%22%2C-7z=64%29\" \r\n" );
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document.write( "Now we have 2 equations in 2 letters to solve:\r\n" );
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document.write( "\"system%285x-4z=33%2C10x-7z=64%29\"\r\n" );
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document.write( "We can eliminate x by multiplying the first equation through by -2\r\n" );
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document.write( "\"system%28-10x%2B8z=-66%2C%22%22%2B10x-7z=%22%22%2B64%29\" \r\n" );
document.write( "        \"z=-2\"\r\n" );
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document.write( "Substitute that in \r\n" );
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document.write( "\"5x-4z=33\"\r\n" );
document.write( "\"5x-4%28-2%29=33\"\r\n" );
document.write( "\"5x%2B8=33\"\r\n" );
document.write( "\"5x=25\"\r\n" );
document.write( "\"x=5\"\r\n" );
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document.write( "Substitute z=-2 and x=5 in any one of the original equations:\r\n" );
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document.write( "\"3x-y-2z=+18\"\r\n" );
document.write( "\"3%285%29-y-2%28-2%29=18%0D%0A%7B%7B%7B15-y%2B4=18\"\r\n" );
document.write( "\"19-y=18\"\r\n" );
document.write( "\"-y=-1\"\r\n" );
document.write( "\"y=1\"\r\n" );
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document.write( "Answer: (x,y,z) = (5,1,-2)\r\n" );
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document.write( "Edwin
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