document.write( "Question 1199042: How do you solve these 3 linear equations using elimination method
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Algebra.Com's Answer #832715 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
How do you solve these 3 linear equations using elimination method
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document.write( "Line up the like symbols:\r\n" );
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document.write( "eq. 1   2x - 3y +   z =  13\r\n" );
document.write( "eq. 2    x +  y -  2z =  -6\r\n" );
document.write( "eq. 3   3x -  y +   z =   8\r\n" );
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document.write( "I notice that the y's will cancel out if I add the middle and bottom\r\n" );
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document.write( "eq. 2    x +  y -  2z =  -6\r\n" );
document.write( "eq. 3   3x -  y +   z =   8\r\n" );
document.write( "        ------------------\r\n" );
document.write( "eq. 4   4x      -   z =   2\r\n" );
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document.write( "I can also make the y's cancel out if I multiply eq. 2 by 3\r\n" );
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document.write( "eq. 5   3x + 3y -  6z = -18\r\n" );
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document.write( "then add eq. 1 to it\r\n" );
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document.write( "eq. 5   3x + 3y -  6z = -18\r\n" );
document.write( "eq. 1   2x - 3y +   z =  13\r\n" );
document.write( "        ------------------\r\n" );
document.write( "eq. 6   5x      -  5z =  -5\r\n" );
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document.write( "I notice that I can divide eq. 6 through by 5\r\n" );
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document.write( "eq. 7    x      -   z =  -1\r\n" );
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document.write( "Now I have two equations with y's eliminated,  \r\n" );
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document.write( "eq. 4   4x      -   z =   2  \r\n" );
document.write( "eq. 7    x      -   z =  -1\r\n" );
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document.write( "I can make the z's cancel if I multiply eq. 7 by -1\r\n" );
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document.write( "eq. 8   -x      +   z =   1\r\n" );
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document.write( "and add it to eq. 4\r\n" );
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document.write( "eq. 4   4x      -   z =   2\r\n" );
document.write( "eq. 8   -x      +   z =   1\r\n" );
document.write( "       --------------------\r\n" );
document.write( "e. 9    3x            =   3\r\n" );
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document.write( "I notice that I can divide eq. 9 through by 3 \r\n" );
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document.write( "eq. 10   x            =   1\r\n" );
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document.write( "Now that I have 1 of the letters, I can switch to\r\n" );
document.write( "substitution. I will use eq. 7\r\n" );
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document.write( "eq. 7    x      -   z =  -1\r\n" );
document.write( "         1      -   z =  -1\r\n" );
document.write( "                   -z =  -2\r\n" );
document.write( "                    z =   2\r\n" );
document.write( "Now that I have 2 of the letters, I can substitute in one\r\n" );
document.write( "of the original equations, say, eq. 2 \r\n" );
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document.write( "eq. 2    x +  y -  2z =  -6\r\n" );
document.write( "         1 +  y -2(2) =  -6\r\n" );
document.write( "         1 +  y -   4 =  -6\r\n" );
document.write( "              y -   3 =  -6\r\n" );
document.write( "                    y =  -3 \r\n" );
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document.write( "(x,y,z) = (1,-3,2)\r\n" );
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document.write( "Edwin
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