document.write( "Question 977247: Solve the system using elimination.
\n" ); document.write( "2x + y = 6
\n" ); document.write( "-x - 2y + 8z = 2
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Algebra.Com's Answer #598772 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Get like letters, equal signs and constants lined up vertically:\r\n" );
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document.write( "(1)   2x +  y      = 6\r\n" );
document.write( "(2)   -x - 2y + 8z = 2\r\n" );
document.write( "(3)   -y + 4z      = 3\r\n" );
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document.write( "We start by observing that z is already eliminated in (1),\r\n" );
document.write( "and that x is already eliminated from (3).\r\n" );
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document.write( "We pick one of those, say (3).  \r\n" );
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document.write( "(3)   -y + 4z      = 3\r\n" );
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document.write( "Since x is already eliminated from (3), we eliminate x from \r\n" );
document.write( "the other two, (1) and (2):\r\n" );
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document.write( "(1)   2x +  y      = 6\r\n" );
document.write( "(2)   -x - 2y + 8z = 2\r\n" );
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document.write( "To do that we multiply (2) by 2 so that the x terms will cancel\r\n" );
document.write( "when we add the equations term by term, getting (4):\r\n" );
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document.write( "(1)   2x +  y       =  6\r\n" );
document.write( "     -2x - 4y + 16z =  4\r\n" );
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document.write( "(4)       -3y + 16z = 10\r\n" );
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document.write( "Now we take (3) and (4) together as a system of 2 equations in\r\n" );
document.write( "only 2 unknowns and line them up vertically:\r\n" );
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document.write( "(3)   -y + 4z  =  3\r\n" );
document.write( "(4)  -3y + 16z = 10\r\n" );
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document.write( "To do that we multiply (3) by -3 so that the y terms will cancel\r\n" );
document.write( "when we add the equations term by term, getting (5):\r\n" );
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document.write( "      3y - 12z = -9\r\n" );
document.write( "(4)  -3y + 16z = 10\r\n" );
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document.write( "            4z = 1\r\n" );
document.write( "(5)          z = 1/4\r\n" );
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document.write( "Using (5), substitute 1/4 for z in (3) to find y:\r\n" );
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document.write( "(3)   -y + 4z  = 3\r\n" );
document.write( "   -y + 4(1/4) = 3\r\n" );
document.write( "        -y + 1 = 3\r\n" );
document.write( "            -y = 2\r\n" );
document.write( "(6)          y = -2\r\n" );
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document.write( "Using (6), substitute -2 for y in (1)\r\n" );
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document.write( "(1)   2x +  y  =  6\r\n" );
document.write( "     2x + (-2) = 6\r\n" );
document.write( "        2x - 2 = 6\r\n" );
document.write( "            2x = 8\r\n" );
document.write( "(7)          x = 4\r\n" );
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document.write( "From (7), (6), and (5), we have the solution \r\n" );
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document.write( "(x,y,z) = (4,-2,1/4)\r\n" );
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document.write( "Edwin

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