document.write( "Question 87119: 2x - y + 2z = -8
\n" ); document.write( "-x + 3y - 4z = 15
\n" ); document.write( " x + 2y - 3z = 9
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #63225 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "2x -  y + 2z = -8\r\n" );
document.write( "-x + 3y - 4z = 15\r\n" );
document.write( " x + 2y - 3z =  9\r\n" );
document.write( "\r\n" );
document.write( "[ 2  -1   2 | -8]\r\n" );
document.write( "[-1   3  -4 | 15]\r\n" );
document.write( "[ 1   2  -3 |  9] \r\n" );
document.write( "\r\n" );
document.write( "Get a zero where the -1 is on the 2nd row is by\r\n" );
document.write( "multiplying the first row by 1 and adding it\r\n" );
document.write( "to 2 times the second row:\r\n" );
document.write( "\r\n" );
document.write( "1[ 2  -1   2 | -8]\r\n" );
document.write( "2[-1   3  -4 | 15]\r\n" );
document.write( " [ 1   2  -3 |  9]\r\n" );
document.write( "\r\n" );
document.write( "[ 2  -1   2 | -8]\r\n" );
document.write( "[ 0   5  -6 | 22]\r\n" );
document.write( "[ 1   2  -3 |  9]\r\n" );
document.write( "\r\n" );
document.write( "Get a zero where the 1 is on the 3rd row is by\r\n" );
document.write( "multiplying the first row by 1 and adding it\r\n" );
document.write( "to -2 times the third row: \r\n" );
document.write( "\r\n" );
document.write( " 1[ 2  -1   2 | -8]\r\n" );
document.write( "  [ 0   5  -6 | 22]\r\n" );
document.write( "-2[ 1   2  -3 |  9]\r\n" );
document.write( "\r\n" );
document.write( "[ 2  -1   2 | -8]\r\n" );
document.write( "[ 0   5  -6 | 22]\r\n" );
document.write( "[ 0  -5   8 |-26]\r\n" );
document.write( "\r\n" );
document.write( "Get a 0 where the -5 is on the third row by\r\n" );
document.write( "multiplying the second row by 1 and adding it\r\n" );
document.write( "to 1 times row 3:\r\n" );
document.write( "\r\n" );
document.write( " [ 2  -1   2 | -8]\r\n" );
document.write( "1[ 0   5  -6 | 22]\r\n" );
document.write( "1[ 0  -5   8 |-26]\r\n" );
document.write( "\r\n" );
document.write( "[ 2  -1   2 | -8]\r\n" );
document.write( "[ 0   5  -6 | 22]\r\n" );
document.write( "[ 0   0   2 | -4]\r\n" );
document.write( "\r\n" );
document.write( "-1,2,-2\r\n" );
document.write( "\r\n" );
document.write( "Get a 1 where the 2 is in the first row by\r\n" );
document.write( "dividing the first row through by 2\r\n" );
document.write( "\r\n" );
document.write( "Get a 1 where the 5 is in the second row by\r\n" );
document.write( "dividing the second row through by 5\r\n" );
document.write( "\r\n" );
document.write( "Get a 1 where the 2 is in the third row by\r\n" );
document.write( "dividing the third row through by 2\r\n" );
document.write( "\r\n" );
document.write( "[ 1   \"-1%2F2\"    1 |  -4]\r\n" );
document.write( "[ 0     1  \"-6%2F5\" | \"22%2F5\"]\r\n" );
document.write( "[ 0     0    1 |  -2]\r\n" );
document.write( "\r\n" );
document.write( "Convert back to three equations:\r\n" );
document.write( "\r\n" );
document.write( "\"x-%281%2F2%29y+%2B+z\" = \"-4\"\r\n" );
document.write( "   \"y-%286%2F5%29z\" = \"22%2F5\"\r\n" );
document.write( "          \"z+=+-2\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute z = -2 into the second equation\r\n" );
document.write( "\r\n" );
document.write( "   \"y-%286%2F5%29%28-2%29\" = \"22%2F5\"\r\n" );
document.write( "\r\n" );
document.write( "   \"y%2B12%2F5\" = \"22%2F5\"\r\n" );
document.write( "\r\n" );
document.write( "       \"y\" = \"22%2F5-12%2F5\"\r\n" );
document.write( "       \"y\" = \"10%2F5\"\r\n" );
document.write( "       \"y\" = \"2\"\r\n" );
document.write( "\r\n" );
document.write( "Finally substitute \"y=2\" and \"z=-2\"\r\n" );
document.write( "into the first equation:\r\n" );
document.write( "\r\n" );
document.write( "\"x-%281%2F2%29y+%2B+z\" = \"-4\"\r\n" );
document.write( "\r\n" );
document.write( "\"x-%281%2F2%29%282%29+%2B+%28-2%29\" = \"-4\"\r\n" );
document.write( "\r\n" );
document.write( "\"x+-+1+-+2+=+-4\"\r\n" );
document.write( "\r\n" );
document.write( "\"x+=+-4%2B1%2B2\"\r\n" );
document.write( "\r\n" );
document.write( "\"x+=+-1\"\r\n" );
document.write( "\r\n" );
document.write( "So the solution is\r\n" );
document.write( "\r\n" );
document.write( "(x, y, z) = (-1, 2, -2)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );