document.write( "Question 1001058: solve the system of three linear equations with three variables
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Algebra.Com's Answer #618349 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Always write systems of equations so that like terms \r\n" );
document.write( "line up vertically, like this:\r\n" );
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document.write( "     5y - 7z = 14\r\n" );
document.write( "2x +  y + 4z = 10\r\n" );
document.write( "2x + 6y - 3z = 30\r\n" );
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document.write( "The first equation contains only 2 letters. That is, \r\n" );
document.write( "x is already eliminated in the first equation.\r\n" );
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document.write( "Therefore we eliminate x from the other two equations:\r\n" );
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document.write( "We multiply the 2nd equation by -1 and add it term\r\n" );
document.write( "by term to the 3rd equation:\r\n" );
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document.write( "-2x -  y - 4z = -10\r\n" );
document.write( " 2x + 6y - 3z =  30\r\n" );
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document.write( "      5y - 7z =  20\r\n" );
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document.write( "Now we put the first equation together with this one\r\n" );
document.write( "and we now have only two equations in only two \r\n" );
document.write( "variables:\r\n" );
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document.write( "     5y - 7z = 14\r\n" );
document.write( "     5y - 7z = 20\r\n" );
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document.write( "We eliminate y by multiplying the second equation by\r\n" );
document.write( "-1 and adding:\r\n" );
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document.write( "     5y - 7z =  14\r\n" );
document.write( "    -5y + 7z = -20    \r\n" );
document.write( "  -----------------\r\n" );
document.write( "          0z = -6\r\n" );
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document.write( "There can be no value of z such that when we multiply\r\n" );
document.write( "by 0 we well get -6, so there is no solution.  The\r\n" );
document.write( "system of equations is said to be INCONSISTENT.\r\n" );
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document.write( "Edwin
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