document.write( "Question 357680: The elimination method can someone help\r
\n" ); document.write( "\n" ); document.write( "3x-2y-z=14
\n" ); document.write( "x-3y-3z=8
\n" ); document.write( "2x-4y-2z=8 \n" ); document.write( "
Algebra.Com's Answer #255364 by Edwin McCravy(20058)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(1)          3x - 2y -  z = 14\r\n" );
document.write( "(2)           x - 3y - 3z =  8\r\n" );
document.write( "(3)          2x - 4y - 2z =  8\r\n" );
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document.write( "Multiply equation (2) by -3\r\n" );
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document.write( "          -3(x - 3y - 3z) = -3(8)\r\n" );
document.write( "            -3x + 9y + 9z = -24\r\n" );
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document.write( "Add it to the equation (1)\r\n" );
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document.write( "(1)          3x - 2y -  z =  14\r\n" );
document.write( "            -3x + 9y + 9z = -24\r\n" );
document.write( "            -------------------\r\n" );
document.write( "(4)               7y + 8z = -10 \r\n" );
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document.write( "---\r\n" );
document.write( "Multiply equation (2) by -2\r\n" );
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document.write( "          -2(x - 3y - 3z) = -2(8)\r\n" );
document.write( "            -2x + 6y + 6z = -16\r\n" );
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document.write( "Add it to the equation (3)\r\n" );
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document.write( "(3)          2x - 4y - 2z =  8\r\n" );
document.write( "            -2x + 6y + 6z = -16\r\n" );
document.write( "            -------------------\r\n" );
document.write( "                  2y + 4z =  -8\r\n" );
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document.write( "Divide that through by 2\r\n" );
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document.write( "(5)               y + 2z =  -4\r\n" );
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document.write( "Now we have a system of 2 equations with only 2 unknowns:\r\n" );
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document.write( "(4)               7y + 8z = -10 \r\n" );
document.write( "(5)                y + 2z =  -4\r\n" );
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document.write( "Multiply eq. (5) by -4\r\n" );
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document.write( "               -4(y + 2z) =  -4(-4)\r\n" );
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document.write( "                 -4y - 8z =  16\r\n" );
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document.write( "add that to eq (4):\r\n" );
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document.write( "(4)               7y + 8z = -10 \r\n" );
document.write( "                 -4y - 8z =  16\r\n" );
document.write( "                 --------------\r\n" );
document.write( "                  3y      =   6\r\n" );
document.write( "                        y = 2\r\n" );
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document.write( " Substitute in eq (4)\r\n" );
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document.write( "                7(2) + 8z = -10\r\n" );
document.write( "                  14 + 8z = -10\r\n" );
document.write( "                       8z = -10-14\r\n" );
document.write( "                       8z = -24\r\n" );
document.write( "                        z = -3   \r\n" );
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document.write( "Substute y = 2 and z = -3 in eq. (1)\r\n" );
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document.write( "(1)          3x - 2y -  z = 14\r\n" );
document.write( "         3x - 2(2) - (-3) = 14\r\n" );
document.write( "               3x - 4 + 3 = 14\r\n" );
document.write( "                   3x - 1 = 14\r\n" );
document.write( "                       3x = 15\r\n" );
document.write( "                        x = 5\r\n" );
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document.write( "So the solution (x,y,z) = (5,2,-3)\r\n" );
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document.write( "Edwin
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