document.write( "Question 814129: Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
\n" ); document.write( "x-y+z=5
\n" ); document.write( "2x+3y-3z=0 \n" ); document.write( "

Algebra.Com's Answer #490165 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( " 1  -1    1   5\r\n" );
document.write( " 2   3   -3   0\r\n" );
document.write( "Add -2 times the first row to the second row:\r\n" );
document.write( " 1  -1    1    5\r\n" );
document.write( " 0   5   -5  -10\r\n" );
document.write( "Multiply the second row by 1/5:\r\n" );
document.write( " 1  -1    1    5\r\n" );
document.write( " 0   1   -1   -2\r\n" );
document.write( "Add the second row to the first:\r\n" );
document.write( " 1   0    0    3\r\n" );
document.write( " 0   1   -1   -2\r\n" );
document.write( "

This is as far as we can go. It translates into:
\n" ); document.write( "x = 3
\n" ); document.write( "y - z = -2 or y = z - 2
\n" ); document.write( "So there are an infinite number of solutions. The x must be 3 but the y and z values can be any numbers which fit either y - z = -2 or y = z - 2.One way to express the solution is: (3, z-2, z) \n" ); document.write( "

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