document.write( "Question 162863: Solve by substitution or elimination:
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Algebra.Com's Answer #120040 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Solve by substitution or elimination:\r\n" );
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document.write( "5x + 2y + 10z =  5\r\n" );
document.write( "3x -  y +  5z = -6\r\n" );
document.write( "2x - 3y -  7z =  5\r\n" );
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document.write( "1. Pick a pair of equations and a letter to eliminate:\r\n" );
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document.write( "I'll pick the first two equations and I'll pick y\r\n" );
document.write( "to eliminate from them:\r\n" );
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document.write( "5x + 2y + 10z =  5\r\n" );
document.write( "3x -  y +  5z = -6\r\n" );
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document.write( "I can eliminate y by multiplying the second equation\r\n" );
document.write( "through by 2 and adding vertically term by term:\r\n" );
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document.write( " 5x + 2y + 10z =   5\r\n" );
document.write( " 6x - 2y + 10z = -12\r\n" );
document.write( "--------------------\r\n" );
document.write( "11x      + 20z =  -7\r\n" );
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document.write( "2. Pick a DIFFERENT pair of equations but the SAME \r\n" );
document.write( "letter to eliminate:  \r\n" );
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document.write( "I'll pick the last two equations and I must eliminate\r\n" );
document.write( "y from them:\r\n" );
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document.write( "3x -  y +  5z = -6\r\n" );
document.write( "2x - 3y -  7z =  5\r\n" );
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document.write( "I can eliminate y by multiplying the upper equation  \r\n" );
document.write( "through by -3 and adding vertically term by term:\r\n" );
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document.write( "-9x + 3y - 15z = 18\r\n" );
document.write( " 2x - 3y -  7z =  5\r\n" );
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document.write( "-7x      - 22z = 23\r\n" );
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document.write( "Next we put those two equations in which we have\r\n" );
document.write( "eliminated y together:\r\n" );
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document.write( "-7x - 22z = 23\r\n" );
document.write( "11x + 20z = -7\r\n" );
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document.write( "We can eliminate x by multiplying the upper\r\n" );
document.write( "equation by 11 and the bottom one by 7\r\n" );
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document.write( "-77x - 242z = 253\r\n" );
document.write( " 77x + 140z = -49\r\n" );
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document.write( "      -102z = 204\r\n" );
document.write( "          z = -2\r\n" );
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document.write( "Substitute z = -2 into \r\n" );
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document.write( "   -7x - 22z =  23\r\n" );
document.write( "-7x - 22(-2) =  23\r\n" );
document.write( "    -7x + 44 =  23\r\n" );
document.write( "         -7x = -21\r\n" );
document.write( "           x = 3\r\n" );
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document.write( "Substitute z = -2 and x = 3 into one\r\n" );
document.write( "of the original three equations:\r\n" );
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document.write( "   3x -  y +  5z = -6\r\n" );
document.write( "3(3) - y + 5(-2) = -6 \r\n" );
document.write( "      9 - y - 10 = -6\r\n" );
document.write( "          -y - 1 = -6\r\n" );
document.write( "              -y = -5\r\n" );
document.write( "               y = 5 \r\n" );
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document.write( "(x, y, z) = (3, 5, -2) \r\n" );
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document.write( "Edwin
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