document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34772>Question 34772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of equations using Gaussian elimination (with a matrix) and back substitution, or by using Gauss-Jordan elimination.\r<BR>\n" );
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document.write( "3x + y - z = 0<BR>\n" );
document.write( "x + y = 2z = 6<BR>\n" );
document.write( "2x + 2y = 3z = 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535544 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=535544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you mean <BR>\n" );
document.write( "3,1,-1,0<BR>\n" );
document.write( "1,1,+2,6<BR>\n" );
document.write( "2,2,+3,10\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 1 by 3/1<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "1,1,2,6<BR>\n" );
document.write( "2,2,3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1/1) *row 1 to row 2<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,2/3,7/3,6<BR>\n" );
document.write( "2,2,3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add  down (-2/1) *row 1 to row 3<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,2/3,7/3,6<BR>\n" );
document.write( "0,4/3,11/3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide row 2 by 2/3<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,21/6,9<BR>\n" );
document.write( "0,4/3,11/3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add  down (-4/3) *row 2 to row 3<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,7/2,9<BR>\n" );
document.write( "0,0,-1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide row 3 by -1/1<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,7/2,9<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add up  (-7/2) *row 3 to row 2<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,0,2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add up  (1/3) *row 3 to row 1<BR>\n" );
document.write( "1,3/9,0,2/3<BR>\n" );
document.write( "0,1,0,2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1/3) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,0<BR>\n" );
document.write( "0,1,0,2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "final<BR>\n" );
document.write( "1,0,0,0<BR>\n" );
document.write( "0,1,0,2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1,0,0,0<BR>\n" );
document.write( "0,1,0,2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
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document.write( "if you mean\r<BR>\n" );
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document.write( "3,1,-1,0<BR>\n" );
document.write( "1,1,-2,6<BR>\n" );
document.write( "2,2,-3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide row 1 by 3/1<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "1,1,-2,6<BR>\n" );
document.write( "2,2,-3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1/1) *row 1 to row 2<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,2/3,-5/3,6<BR>\n" );
document.write( "2,2,-3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add  down (-2/1) *row 1 to row 3<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,2/3,-5/3,6<BR>\n" );
document.write( "0,4/3,-7/3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide row 2 by 2/3<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,-15/6,9<BR>\n" );
document.write( "0,4/3,-7/3,10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add  down (-4/3) *row 2 to row 3<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,-5/2,9<BR>\n" );
document.write( "0,0,1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide row 3 by 1/1<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,-5/2,9<BR>\n" );
document.write( "0,0,1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add up  (5/2) *row 3 to row 2<BR>\n" );
document.write( "1,1/3,-1/3,0<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add up  (1/3) *row 3 to row 1<BR>\n" );
document.write( "1,3/9,0,-2/3<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1/3) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,-2<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "final<BR>\n" );
document.write( "1,0,0,-2<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1,0,0,-2<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );