document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=899715>Question 899715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of linear equations using the Gauss-Jordan elimination method.<BR>\n" );
document.write( "x	 + 	y	 + 	z	 = 	0<BR>\n" );
document.write( "2x	 &#8722; 	y	 + 	z	 = 	1<BR>\n" );
document.write( "x	 + 	y	 &#8722; 	2z	 = 	2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #545565 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=545565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1,1,1,0<BR>\n" );
document.write( "2,-1,1,1<BR>\n" );
document.write( "1,1,-2,2\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-2) *row 1 to row 2<BR>\n" );
document.write( "1,1,1,0<BR>\n" );
document.write( "0,-3,-1,1<BR>\n" );
document.write( "1,1,-2,2\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1) *row 1 to row 3<BR>\n" );
document.write( "1,1,1,0<BR>\n" );
document.write( "0,-3,-1,1<BR>\n" );
document.write( "0,0,-3,2\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 2 by -3<BR>\n" );
document.write( "1,1,1,0<BR>\n" );
document.write( "0,1,-1/-3,1/-3<BR>\n" );
document.write( "0,0,-3,2\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (0) *row 2 to row 3<BR>\n" );
document.write( "1,1,1,0<BR>\n" );
document.write( "0,1,1/3,1/-3<BR>\n" );
document.write( "0,0,-3,2\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 3 by -3<BR>\n" );
document.write( "1,1,1,0<BR>\n" );
document.write( "0,1,1/3,1/-3<BR>\n" );
document.write( "0,0,1,2/-3\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  (-1/3) *row 3 to row 2<BR>\n" );
document.write( "1,1,1,0<BR>\n" );
document.write( "0,1,0,-3/27<BR>\n" );
document.write( "0,0,1,2/-3\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1) *row 3 to row 1<BR>\n" );
document.write( "1,1,0,-2/-3<BR>\n" );
document.write( "0,1,0,-1/9<BR>\n" );
document.write( "0,0,1,2/-3\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,21/27<BR>\n" );
document.write( "0,1,0,-1/9<BR>\n" );
document.write( "0,0,1,2/-3\r<BR>\n" );
document.write( "\n" );
document.write( "final<BR>\n" );
document.write( "1,0,0,7/9<BR>\n" );
document.write( "0,1,0,-1/9<BR>\n" );
document.write( "0,0,1,2/-3\r<BR>\n" );
document.write( "\n" );
document.write( "1,0,0,7/9 = 0.77777778<BR>\n" );
document.write( "0,1,0,-1/9 = -0.11111111<BR>\n" );
document.write( "0,0,1,-2/3 = -0.66666667<BR>\n" );
document.write( "\"7/9\",\"-1/9\",\"-2/3\"<BR>\n" );
document.write( "(7/9,-1/9,-2/3)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );