document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907712>Question 907712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x+y+z-w=5<BR>\n" );
document.write( "2x+y-z+w=6<BR>\n" );
document.write( "x-5y+3z+w=9<BR>\n" );
document.write( "-x-y+z+4w=7\r<BR>\n" );
document.write( "\n" );
document.write( "These always confuse me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550512 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1,1,1,-1,5<BR>\n" );
document.write( "2,1,-1,1,6<BR>\n" );
document.write( "1,-5,3,1,9<BR>\n" );
document.write( "-1,-1,1,4,7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add  down (-2) *row 1 to row 2<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,-1,-3,3,-4<BR>\n" );
document.write( "1,-5,3,1,9<BR>\n" );
document.write( "-1,-1,1,4,7\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1) *row 1 to row 3<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,-1,-3,3,-4<BR>\n" );
document.write( "0,-6,2,2,4<BR>\n" );
document.write( "-1,-1,1,4,7\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (1) *row 1 to row 4<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,-1,-3,3,-4<BR>\n" );
document.write( "0,-6,2,2,4<BR>\n" );
document.write( "0,0,2,3,12\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 2 by -1<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,-3,4<BR>\n" );
document.write( "0,-6,2,2,4<BR>\n" );
document.write( "0,0,2,3,12\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (6) *row 2 to row 3<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,-3,4<BR>\n" );
document.write( "0,0,20,-16,28<BR>\n" );
document.write( "0,0,2,3,12\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (0) *row 2 to row 4<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,-3,4<BR>\n" );
document.write( "0,0,20,-16,28<BR>\n" );
document.write( "0,0,2,3,12\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 3 by 20<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,-3,4<BR>\n" );
document.write( "0,0,1,-16/20,28/20<BR>\n" );
document.write( "0,0,2,3,12\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-2) *row 3 to row 4<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,-3,4<BR>\n" );
document.write( "0,0,1,-4/5,7/5<BR>\n" );
document.write( "0,0,0,23/5,46/5\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 4 by 23/5<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,-3,4<BR>\n" );
document.write( "0,0,1,-4/5,7/5<BR>\n" );
document.write( "0,0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "We now have the value for the last variable.<BR>\n" );
document.write( "We will work our way up and get the other solutions.\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (4/5) *row 4 to row 3<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,-3,4<BR>\n" );
document.write( "0,0,1,0,3<BR>\n" );
document.write( "0,0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (3) *row 4 to row 2<BR>\n" );
document.write( "1,1,1,-1,5<BR>\n" );
document.write( "0,1,3,0,10<BR>\n" );
document.write( "0,0,1,0,3<BR>\n" );
document.write( "0,0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (1) *row 4 to row 1<BR>\n" );
document.write( "1,1,1,0,7<BR>\n" );
document.write( "0,1,3,0,10<BR>\n" );
document.write( "0,0,1,0,3<BR>\n" );
document.write( "0,0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-3) *row 3 to row 2<BR>\n" );
document.write( "1,1,1,0,7<BR>\n" );
document.write( "0,1,0,0,1<BR>\n" );
document.write( "0,0,1,0,3<BR>\n" );
document.write( "0,0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1) *row 3 to row 1<BR>\n" );
document.write( "1,1,0,0,4<BR>\n" );
document.write( "0,1,0,0,1<BR>\n" );
document.write( "0,0,1,0,3<BR>\n" );
document.write( "0,0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,0,3<BR>\n" );
document.write( "0,1,0,0,1<BR>\n" );
document.write( "0,0,1,0,3<BR>\n" );
document.write( "0,0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "final\r<BR>\n" );
document.write( "\n" );
document.write( "1,0,0,0,3<BR>\n" );
document.write( "0,1,0,0,1<BR>\n" );
document.write( "0,0,1,0,3<BR>\n" );
document.write( "0,0,0,1,2<BR>\n" );
document.write( "\"3\",\"1\",\"3\",\"2\"<BR>\n" );
document.write( "(3,1,3,2)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );