document.write( "Question 472276: I have started the problem but am lost as to how to continue.
\n" ); document.write( "4x − y = 2
\n" ); document.write( "8x + 10y = −4\r
\n" ); document.write( "\n" ); document.write( "This was the problem I was given and was asked to use the Gauss-Jordan method to find the solution to the system of equations. \r
\n" ); document.write( "\n" ); document.write( "So far I did the first step but I need help understanding the steps that follow. \n" ); document.write( "
Algebra.Com's Answer #323826 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "your original equations are as follows:\r\n" );
document.write( "4x − y = 2\r\n" );
document.write( "8x + 10y = −4 \r\n" );
document.write( "your matrix would look like the following:\r\n" );
document.write( "\r\n" );
document.write( "              4      -1       2\r\n" );
document.write( "              8       10     -4\r\n" );
document.write( "\r\n" );
document.write( "multiply the first row by 2 and subtract it from the second row to get:\r\n" );
document.write( "\r\n" );
document.write( "              4       -1        2\r\n" );
document.write( "              0       12       -8\r\n" );
document.write( "\r\n" );
document.write( "divide the second row by 12 and add it to the first row to get:\r\n" );
document.write( "\r\n" );
document.write( "              4        0        16/12\r\n" );
document.write( "              0       12       -8\r\n" );
document.write( "\r\n" );
document.write( "multiply the first row by 1/4 and multiply the second row by 1/12 to get:\r\n" );
document.write( "\r\n" );
document.write( "              1        0        4/12\r\n" );
document.write( "              0        1        -8/12\r\n" );
document.write( "\r\n" );
document.write( "your answer should be x = 4/12 and y = -8/12\r\n" );
document.write( "\r\n" );
document.write( "plug those values into your original equation to get:\r\n" );
document.write( "\r\n" );
document.write( "4x − y = 2\r\n" );
document.write( "8x + 10y = −4 \r\n" );
document.write( "\r\n" );
document.write( "become:\r\n" );
document.write( "16/12 - (-8/12) = 2\r\n" );
document.write( "32/12 - 80/12 = -4\r\n" );
document.write( "\r\n" );
document.write( "these become:\r\n" );
document.write( "24/12 = 2\r\n" );
document.write( "-48/12 = -4\r\n" );
document.write( "\r\n" );
document.write( "these become:\r\n" );
document.write( "2 = 2\r\n" );
document.write( "-4 = -4\r\n" );
document.write( "\r\n" );
document.write( "the original equations are confirmed to be true, establishing the solutions as good.\r\n" );
document.write( "\r\n" );
document.write( "the gauss-jordan method takes gaussian elimination method one step further by making the elements on the left hand side of the matrix all equal to 1.\r\n" );
document.write( "this eliminates having to go back and solve for each of the variables in turn.\r\n" );
document.write( "

\n" ); document.write( "a reference on the gauss-jordan elimination method is shown below.
\n" ); document.write( "http://ceee.rice.edu/Books/CS/chapter2/linear44.html
\n" ); document.write( " \n" ); document.write( "
\n" );