document.write( "Question 51076This question is from textbook finate mathematics
\n" ); document.write( ": Please use the Gauss-Jordan method to solve system of equations
\n" ); document.write( "23. 6x-3y = 1
\n" ); document.write( " -12x-6y= -2
\n" ); document.write( "I thought this one is no solution but the answer (back of the book) is ((23y + 1)/6,y). Why?\r
\n" ); document.write( "\n" ); document.write( "29. 4x+4y-4z = 24
\n" ); document.write( " 2x-y+z =-9
\n" ); document.write( " x-2y+3z = 1\r
\n" ); document.write( "\n" ); document.write( "Thanks.
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Algebra.Com's Answer #34050 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Please use the Gauss-Jordan method to solve system of equations\r\n" );
document.write( "23.   6x-3y = 1\r\n" );
document.write( "     -12x-6y= -2\r\n" );
document.write( "I thought this one is no solution but the answer (back of the book)\r\n" );
document.write( "is ((23y + 1)/6,y).  Why?\r\n" );
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document.write( "The system you typed has solution (1/6, 0).  Either you mistyped the\r\n" );
document.write( "problem or the book is wrong.\r\n" );
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document.write( "A similar system that would have the solution you gave would be:\r\n" );
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document.write( "      6x-23y = 1\r\n" );
document.write( "      -12x+46y= -2\r\n" );
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document.write( "29.  4x + 4y - 4z = 24\r\n" );
document.write( "     2x -  y +  z = -9\r\n" );
document.write( "      x - 2y + 3z =  1\r\n" );
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document.write( "[4   4  -4 | 24]\r\n" );
document.write( "[2  -1   1 | -9]\r\n" );
document.write( "[1  -2   3 |  1]\r\n" );
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document.write( "Divide row 1 thru by 4\r\n" );
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document.write( "[4   4  -4 | 24]÷(4)\r\n" );
document.write( "[2  -1   1 | -9]\r\n" );
document.write( "[1  -2   3 |  1]\r\n" );
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document.write( "[1   1  -1 |  6]\r\n" );
document.write( "[2  -1   1 | -9]\r\n" );
document.write( "[1  -2   3 |  1]\r\n" );
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document.write( "Get a 0 where the 2 is by multiplying row 1 by -2\r\n" );
document.write( "and adding it to row 2\r\n" );
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document.write( "[2 -1 1|-9]+(-2)·[1 1 -1|6] = [2 -1 1|-9]+[-2 -2 2|-12] = [0 -3 3|-21] \r\n" );
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document.write( "[1   1  -1 |   6]\r\n" );
document.write( "[0  -3   3 | -21]\r\n" );
document.write( "[1  -2   3 |   1]\r\n" );
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document.write( "Divide row 2 thru by -3\r\n" );
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document.write( "[1   1  -1 |   6]\r\n" );
document.write( "[0   1  -1 |   7]\r\n" );
document.write( "[1  -2   3 |   1]\r\n" );
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document.write( "Get a 0 where the 1 is in row 3 column 1 by multiplying \r\n" );
document.write( "row 1 by -1 and adding to row 3:\r\n" );
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document.write( "[1 -2 3|1]+(-1)[1 1 -1|6] = [1 -2 3|1]+[-1 -1 1|-6] = [0 -3 4|-5]\r\n" );
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document.write( "[1   1  -1 |   6]\r\n" );
document.write( "[0   1  -1 |   7]\r\n" );
document.write( "[0  -3   4 |  -5]\r\n" );
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document.write( "Get a 0 where the -3 is by multiplying row 2 by 3 and adding to\r\n" );
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document.write( "[0 -3 4|-5]+(3)[0 1 -1|7] = [0 -3 4|-5]+[0 3 -3|21] = [0 0 1|16]\r\n" );
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document.write( "[1   1  -1 |   6]\r\n" );
document.write( "[0   1  -1 |   7]\r\n" );
document.write( "[0   0   1 |  16]\r\n" );
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document.write( "This matrix represents this system:\r\n" );
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document.write( "1x + 1y - 1z =  6\r\n" );
document.write( "0x + 1y - 1z =  7\r\n" );
document.write( "0x + 0y + 1z = 16\r\n" );
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document.write( "or\r\n" );
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document.write( " x +  y -  z =  6\r\n" );
document.write( "      y -  z =  7\r\n" );
document.write( "           z = 16\r\n" );
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document.write( "Now back-substitute:\r\n" );
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document.write( "Substitute 16 for z in the 2nd equation:\r\n" );
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document.write( "       y - z = 7\r\n" );
document.write( "      y - 16 = 7\r\n" );
document.write( "           y = 23\r\n" );
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document.write( "Substitute 23 for y and 16 for z in the 1st equation:\r\n" );
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document.write( "   x + y - z = 6\r\n" );
document.write( " x + 23 - 16 = 6\r\n" );
document.write( "       x + 7 = 6\r\n" );
document.write( "           x = -1\r\n" );
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document.write( "So the solution is (x, y, z) = (-1, 23, 16)\r\n" );
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document.write( "Edwin
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