document.write( "Question 1152659: 6x+z=21
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\n" ); document.write( "-5y+6z=-33 \n" ); document.write( "
Algebra.Com's Answer #774703 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Line the equations up so that the letters line up vertically,\r\n" );
document.write( "like this:\r\n" );
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document.write( "6x +       z =  21\r\n" );
document.write( "4x + 6y      =  34\r\n" );
document.write( "    -5y + 6z = -33\r\n" );
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document.write( "Notice that y is already eliminated from the first equation,\r\n" );
document.write( "z is already eliminated from the second equation and x is\r\n" );
document.write( "already eliminated from the third equation.  We need two\r\n" );
document.write( "equations with the SAME letter eliminated from them.  So we\r\n" );
document.write( "pick the easiest two equations to eliminate a letter from.\r\n" );
document.write( "We pick the 1st and 3rd to eliminate z from:\r\n" );
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document.write( "6x +        z =  21\r\n" );
document.write( "     -5y + 6z = -33\r\n" );
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document.write( "We multiply the top equation through by -6 to make it cancel\r\n" );
document.write( "with the bottom equation, Then we add vertically term-by-term\r\n" );
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document.write( "-36x +      -6z = -126\r\n" );
document.write( "       -5y + 6z =  -33\r\n" );
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document.write( "-36x -  5y      = -159\r\n" );
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document.write( "Since we have eliminated z, and the original second equation also\r\n" );
document.write( "has z eliminated we put those two together:\r\n" );
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document.write( "  4x + 6y  =   34\r\n" );
document.write( "-36x - 5y  = -159\r\n" );
document.write( "-----------------\r\n" );
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document.write( "We can make the x's cancel by multiplying the top equation by 9\r\n" );
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document.write( " 36x + 54y  =  306\r\n" );
document.write( "-36x -  5y  = -159\r\n" );
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document.write( "       49y  =  147\r\n" );
document.write( "         y  =  147/49\r\n" );
document.write( "         y  =   3\r\n" );
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document.write( "Substitute y = 3 into \r\n" );
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document.write( "     4x + 6y = 34\r\n" );
document.write( "   4x + 6(3) = 34\r\n" );
document.write( "     4x + 18 = 34\r\n" );
document.write( "          4x = 16\r\n" );
document.write( "           x = 4\r\n" );
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document.write( "Substitute x = 4 into the original first equation:\r\n" );
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document.write( "      6x + z = 21 \r\n" );
document.write( "    6(4) + z = 21\r\n" );
document.write( "      24 + z = 21 \r\n" );
document.write( "           z = -3\r\n" );
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document.write( "So the solution is (x, y, z) = (4, 3, -3)\r\n" );
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document.write( "Edwin
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