document.write( "Question 770538: solve using elimination/addition.\r
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\n" ); document.write( "x-y+4z=-21 \n" ); document.write( "
Algebra.Com's Answer #469647 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(1)        x +  y +  z =  -5\r\n" );
document.write( "(2)       2x + 3y - 2z =   8\r\n" );
document.write( "(3)        x -  y + 4z = -21\r\n" );
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document.write( "We can eliminate y by adding \r\n" );
document.write( "  (1) and (3) term by term\r\n" );
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document.write( "(1)        x +  y +  z =  -5\r\n" );
document.write( "(3)        x -  y + 4z = -21\r\n" );
document.write( "----------------------------\r\n" );
document.write( "(4)       2x      + 5z = -26\r\n" );
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document.write( "We can eliminate y from (2) and (3)\r\n" );
document.write( "by multiplying (3) by -3  and adding\r\n" );
document.write( "to (2)\r\n" );
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document.write( "         3x - 3y + 12z = -63 \r\n" );
document.write( "(2)      2x + 3y -  2z =   8\r\n" );
document.write( "----------------------------\r\n" );
document.write( "         5x      + 10z = -55\r\n" );
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document.write( "And we can divide that through by 5:\r\n" );
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document.write( "(5)       x + 2z = -11\r\n" );
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document.write( "So now we have the 2 by 2 system \r\n" );
document.write( "of (4) and (5)\r\n" );
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document.write( "(4)      2x + 5z = -26\r\n" );
document.write( "(5)       x + 2z = -11\r\n" );
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document.write( "Multiply (5) by -2 and add to (4)\r\n" );
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document.write( "        -2x - 4z =  22\r\n" );
document.write( "(4)      2x + 5z = -26\r\n" );
document.write( "         -------------\r\n" );
document.write( "(6)            z =  -4\r\n" );
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document.write( "Substitute z = -4 in (5)\r\n" );
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document.write( "(5)       x + 2z = -11\r\n" );
document.write( "       x + 2(-4) = -11\r\n" );
document.write( "           x - 8 = -11\r\n" );
document.write( "               x = -3\r\n" );
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document.write( "Substitute x = -3 and z = -4 in (1)\r\n" );
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document.write( "(1)         x + y + z = -5\r\n" );
document.write( "        -3 + y + (-4) = -5 \r\n" );
document.write( "                y - 7 = -5\r\n" );
document.write( "                    y =  2\r\n" );
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document.write( "So solution is (x,y,z) = (-3,2,-4)\r\n" );
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document.write( "Edwin
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