document.write( "Question 448111: Solve the system by the method of elimination.\r
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\n" ); document.write( "3y+z=-8 \n" ); document.write( "

Algebra.Com's Answer #308455 by Edwin McCravy(20056) $\"\"$ $\"About$

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Solve the system by the method of elimination.
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document.write( " x - 2y + 3z = 11\r\n" );
document.write( "2x      -  z =  3\r\n" );
document.write( "     3y +  z = -8\r\n" );
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document.write( "The 2nd equation is the simplest\r\n" );
document.write( "and it already has y eliminated in it.\r\n" );
document.write( "so let's eliminate y also from the 1st \r\n" );
document.write( "and 3rd, so we'll have two equations \r\n" );
document.write( "with y eliminated in them:\r\n" );
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document.write( "To eliminate y from the 1st and 3rd equations,\r\n" );
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document.write( " x - 2y + 3z = 11\r\n" );
document.write( "     3y +  z = -8\r\n" );
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document.write( "we multiply the top one by 3 and the bottom one by 2\r\n" );
document.write( "and add them, and the y's will cancel out:\r\n" );
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document.write( "3x - 6y +  9z =  33\r\n" );
document.write( "     6y +  2z = -16\r\n" );
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document.write( "3x      + 11z =  17\r\n" );
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document.write( "So we put that with the original second equation:\r\n" );
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document.write( "3x + 11z =  17\r\n" );
document.write( "2x -   z =   3\r\n" );
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document.write( "To eliminate z we multiply the bottom one\r\n" );
document.write( "through by 11, and add them so the z's will\r\n" );
document.write( "cancel out:\r\n" );
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document.write( " 3x + 11z =  17\r\n" );
document.write( "22x - 11z =  33\r\n" );
document.write( "---------------\r\n" );
document.write( "25x       =  50\r\n" );
document.write( "        x =   2\r\n" );
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document.write( "Substitute that in \r\n" );
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document.write( "  2x - z =  3\r\n" );
document.write( "2(2) - z =  3 \r\n" );
document.write( "   4 - z =  3\r\n" );
document.write( "      -z = -1\r\n" );
document.write( "       z =  1  \r\n" );
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document.write( "Substitute that in\r\n" );
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document.write( "     3y +  z = -8\r\n" );
document.write( "      3y + 1 = -8\r\n" );
document.write( "          3y = -9\r\n" );
document.write( "           y = -3\r\n" );
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document.write( "(x,y,z) = (2,-3,1)\r\n" );
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document.write( "Edwin

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