document.write( "Question 556914: 
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document.write( "Solve the system:\r\n" );
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document.write( "-x + 2y - 6z = 4\r\n" );
document.write( " x +  y + 2z = 3\r\n" );
document.write( "2x + 3y + 2z = 5\r\n" );
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document.write( "What does the answer mean graphically?\r\n" );
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Algebra.Com's Answer #362346 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "-x + 2y - 6z = 4\r\n" );
document.write( " x +  y + 2z = 3\r\n" );
document.write( "2x + 3y + 2z = 5\r\n" );
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document.write( "Eliminate x from the first two equations simply by adding them\r\n" );
document.write( "like term by like term\r\n" );
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document.write( "-x + 2y - 6z = 4\r\n" );
document.write( " x +  y + 2z = 3\r\n" );
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document.write( "     3y - 4z = 7\r\n" );
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document.write( "Eliminate x from the first and third equations simply by multiplying\r\n" );
document.write( "the first equation by 2\r\n" );
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document.write( "-2x + 4y - 12z = 8\r\n" );
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document.write( "and add it to the original third equation term by like term\r\n" );
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document.write( " 2x + 3y +  2z = 5\r\n" );
document.write( "-2x + 4y - 12z = 8\r\n" );
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document.write( "      7y - 10z = 13\r\n" );
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document.write( "Now we put the two equations without x together\r\n" );
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document.write( "      3y -  4z =  7\r\n" );
document.write( "      7y - 10z = 13\r\n" );
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document.write( "Eliminate z from those two equations by multiplying the first\r\n" );
document.write( "one by -5 and the second one by 2, and adding term by term:\r\n" );
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document.write( "     -15y + 20z = -35\r\n" );
document.write( "      14y - 20z =  26\r\n" );
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document.write( "       -y       =  -9\r\n" );
document.write( "              y = 9\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "       7y - 10z =  13\r\n" );
document.write( "     7(9) - 10z =  13\r\n" );
document.write( "       63 - 10z =  13\r\n" );
document.write( "           -10z = -50   \r\n" );
document.write( "              z = 5\r\n" );
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document.write( "Substitute 9 for y and 5 for z in one of the\r\n" );
document.write( "original equations, say the second one:\r\n" );
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document.write( "   x + y + 2z = 3\r\n" );
document.write( " x + 9 + 2(5) = 3  \r\n" );
document.write( "   x + 9 + 10 = 3\r\n" );
document.write( "       x + 19 = 3 \r\n" );
document.write( "            x = -16\r\n" );
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document.write( "(x,y,z) = (-16,9,5)\r\n" );
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document.write( "Graphically that means that three planes intersect in the\r\n" );
document.write( "3-dimensional point (-16,9,5)\r\n" );
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document.write( "Edwin

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