\r\n" );
document.write( "This comes out with very terrible answers, so I'll bet anything\r\n" );
document.write( "you copied something wrong, like a number or a sign. So you'll\r\n" );
document.write( "probably have to do it over after correcting your error of \r\n" );
document.write( "copying, because the tiniest error in a problem like this will\r\n" );
document.write( "make the answers come out terrible. But here it is exactly\r\n" );
document.write( "as you copied it.\r\n" );
document.write( "\r\n" );
document.write( "Line up the terms with like letters under like letters,\r\n" );
document.write( "like this: \r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Put in all the understood zero terms for missing letters\r\n" );
document.write( "and understood 1 coefficients:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Move the - signs close to the terms, erase the + signs\r\n" );
document.write( "and all the letters and put a vertical line where the\r\n" );
document.write( "= signs are. Then enclose the whole thing in parentheses.\r\n" );
document.write( "This is called an augmented matrix, augmented because of\r\n" );
document.write( "the vertical line:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "It's easier if you have a 1 as the upper left element.\r\n" );
document.write( "So we switch the 1st and 3rd rows. We write that operation as\r\n" );
document.write( "R1<->R3\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "To get a 0 where the 3 is in the 2nd row, 1st column, multiply\r\n" );
document.write( "R1 by -3 and add R2 to it:\r\n" );
document.write( "\r\n" );
document.write( " -3 -6 0 -6 | 30\r\n" );
document.write( " 3 2 0 -1 | -3\r\n" );
document.write( " ------------------------\r\n" );
document.write( " 0 -4 0 -7 | -33\r\n" );
document.write( "\r\n" );
document.write( "Now replace R2 by that. This operation is written as\r\n" );
document.write( "\r\n" );
document.write( "-3R1+R2->R2\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "--\r\n" );
document.write( "To get a 0 where the 2 is in the 3rd row, 1st column, multiply\r\n" );
document.write( "R1 by -2 and add R3 to it:\r\n" );
document.write( "\r\n" );
document.write( " -2 -4 0 -4 | -20\r\n" );
document.write( " 2 -1 4 1 | -2\r\n" );
document.write( " ------------------------\r\n" );
document.write( " 0 -5 4 -3 | -22\r\n" );
document.write( "\r\n" );
document.write( "Now replace R3 by that. This operation is written as\r\n" );
document.write( "\r\n" );
document.write( "-2R1+R2->R2\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "--\r\n" );
document.write( "To get a 0 where the 1 is in the 4th row, 1st column, multiply\r\n" );
document.write( "R1 by -1 and add R4 to it:\r\n" );
document.write( "\r\n" );
document.write( " -1 -2 0 -2 | -10\r\n" );
document.write( " 1 1 2 0 | -2\r\n" );
document.write( " ------------------------\r\n" );
document.write( " 0 -1 2 -2 | -12\r\n" );
document.write( "\r\n" );
document.write( "Now replace R4 by that. This operation is written as\r\n" );
document.write( "\r\n" );
document.write( "-1R1+R4->R4\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Now we work on the second column. Things will be easier\r\n" );
document.write( "if we can get a 1 where the -4 is on the 2nd row 2nd column.\r\n" );
document.write( "So we multiply R3 by -1 and swap it with R2.\r\n" );
document.write( "\r\n" );
document.write( "That operation is written as\r\n" );
document.write( "\r\n" );
document.write( "-R4<->R2\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "-----------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "To get a 0 where the -5 is in the 3rd row, 2nd column, multiply\r\n" );
document.write( "R2 by 5 and add R3 to it:\r\n" );
document.write( "\r\n" );
document.write( " 0 5 -10 10 | 60\r\n" );
document.write( " 0 -5 4 -3 | -22\r\n" );
document.write( " ------------------------\r\n" );
document.write( " 0 0 -6 7 | 38\r\n" );
document.write( "\r\n" );
document.write( "Now replace R3 by that. This operation is written as\r\n" );
document.write( "\r\n" );
document.write( "-5R2+R3->R3\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "--\r\n" );
document.write( "To get a 0 where the -4 is in the 4th row, 2nd column, multiply\r\n" );
document.write( "R2 by 4 and add R4 to it:\r\n" );
document.write( "\r\n" );
document.write( " 0 4 -8 8 | 48\r\n" );
document.write( " 0 -4 0 -7 | -33\r\n" );
document.write( " ------------------------\r\n" );
document.write( " 0 0 -8 1 | 15\r\n" );
document.write( "\r\n" );
document.write( "Now replace R4 by that. This operation is written as\r\n" );
document.write( "\r\n" );
document.write( "-4R2+R4->R4\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "To get a 0 where the -8 is in the 4th row, 3rd column, multiply\r\n" );
document.write( "R3 by 4, and add -3 times R4 to it:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 0 0 -24 28 | 152\r\n" );
document.write( " 0 0 24 -3 | -45\r\n" );
document.write( " ------------------------\r\n" );
document.write( " 0 0 0 25 | 107\r\n" );
document.write( "\r\n" );
document.write( "Now replace R4 by that. This operation is written as\r\n" );
document.write( "\r\n" );
document.write( "-4R2-3R4->R4\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Convert the augmented matrix back to a system of equations:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Get rid of the understood 0 terms and 1 coefficients:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Solve the 4th equation to find t\r\n" );
document.write( "\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Substitute in the 3rd equation to find z\r\n" );
document.write( "\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "Clear of fractions by multiplying through by 25\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "Reduce the fraction:\r\n" );
document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Substitute in the 2nd equation to find y\r\n" );
document.write( "\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "Clear of fractions by multiplying through by 50\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "Reduce the fraction:\r\n" );
document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Substitute in the 1st equation to find x\r\n" );
document.write( "\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "Clear of fractions by multiplying through by 25\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "So the terrible solution is\r\n" );
document.write( "\r\n" );
document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Now find your mistake in copying the problem and\r\n" );
document.write( "re-do it with the correction.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "