document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=903022>Question 903022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2a + 3b + c + 2d = 20<BR>\n" );
document.write( "4a + b + 2c + 5d = 50<BR>\n" );
document.write( "a + 2b + 3c + d = 10<BR>\n" );
document.write( "2a + 4b + 2c + 3d = 15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547703 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=547703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> gauss jordan<BR>\n" );
document.write( "2,3,1,2,20<BR>\n" );
document.write( "4,1,2,5,50<BR>\n" );
document.write( "1,2,3,1,10<BR>\n" );
document.write( "2,4,2,3,15\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 1 by 2<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "4,1,2,5,50<BR>\n" );
document.write( "1,2,3,1,10<BR>\n" );
document.write( "2,4,2,3,15\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-4) *row 1 to row 2<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,-5,0,1,10<BR>\n" );
document.write( "1,2,3,1,10<BR>\n" );
document.write( "2,4,2,3,15\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1) *row 1 to row 3<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,-5,0,1,10<BR>\n" );
document.write( "0,1/2,5/2,0,0<BR>\n" );
document.write( "2,4,2,3,15\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-2) *row 1 to row 4<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,-5,0,1,10<BR>\n" );
document.write( "0,1/2,5/2,0,0<BR>\n" );
document.write( "0,1,1,1,-5\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 2 by -5<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,1/-5,-2<BR>\n" );
document.write( "0,1/2,5/2,0,0<BR>\n" );
document.write( "0,1,1,1,-5\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1/2) *row 2 to row 3<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,1/-5,-2<BR>\n" );
document.write( "0,0,10/4,-1/-10,1<BR>\n" );
document.write( "0,1,1,1,-5\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1) *row 2 to row 4<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,1/-5,-2<BR>\n" );
document.write( "0,0,5/2,1/10,1<BR>\n" );
document.write( "0,0,1,-6/-5,-3\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 3 by 5/2<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,1/-5,-2<BR>\n" );
document.write( "0,0,1,2/50,2/5<BR>\n" );
document.write( "0,0,1,6/5,-3\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1) *row 3 to row 4<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,1/-5,-2<BR>\n" );
document.write( "0,0,1,1/25,2/5<BR>\n" );
document.write( "0,0,0,145/125,-17/5\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 4 by 29/25<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,1/-5,-2<BR>\n" );
document.write( "0,0,1,1/25,2/5<BR>\n" );
document.write( "0,0,0,1,-425/145\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  (-1/25) *row 4 to row 3<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,1/-5,-2<BR>\n" );
document.write( "0,0,1,0,1875/3625<BR>\n" );
document.write( "0,0,0,1,-85/29\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1/-5) *row 4 to row 2<BR>\n" );
document.write( "1,3/2,1/2,1,10<BR>\n" );
document.write( "0,1,0,0,375/-145<BR>\n" );
document.write( "0,0,1,0,15/29<BR>\n" );
document.write( "0,0,0,1,-85/29\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1) *row 4 to row 1<BR>\n" );
document.write( "1,3/2,1/2,0,375/29<BR>\n" );
document.write( "0,1,0,0,75/-29<BR>\n" );
document.write( "0,0,1,0,15/29<BR>\n" );
document.write( "0,0,0,1,-85/29\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (0) *row 3 to row 2<BR>\n" );
document.write( "1,3/2,1/2,0,375/29<BR>\n" );
document.write( "0,1,0,0,2175/-841<BR>\n" );
document.write( "0,0,1,0,15/29<BR>\n" );
document.write( "0,0,0,1,-85/29\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1/2) *row 3 to row 1<BR>\n" );
document.write( "1,6/4,0,0,21315/1682<BR>\n" );
document.write( "0,1,0,0,75/-29<BR>\n" );
document.write( "0,0,1,0,15/29<BR>\n" );
document.write( "0,0,0,1,-85/29\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-3/2) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,0,-55680/-3364<BR>\n" );
document.write( "0,1,0,0,75/-29<BR>\n" );
document.write( "0,0,1,0,15/29<BR>\n" );
document.write( "0,0,0,1,-85/29\r<BR>\n" );
document.write( "\n" );
document.write( "final<BR>\n" );
document.write( "1,0,0,0,480/29<BR>\n" );
document.write( "0,1,0,0,75/-29<BR>\n" );
document.write( "0,0,1,0,15/29<BR>\n" );
document.write( "0,0,0,1,-85/29\r<BR>\n" );
document.write( "\n" );
document.write( "1,0,0,0,480/29 = 16.5517241<BR>\n" );
document.write( "0,1,0,0,75/-29 = -2.5862069<BR>\n" );
document.write( "0,0,1,0,15/29 = 0.51724138<BR>\n" );
document.write( "0,0,0,1,-85/29 = -2.93103448<BR>\n" );
document.write( "\"480/29\",\"75/-29\",\"15/29\",\"-85/29\"<BR>\n" );
document.write( "(480/29,75/-29,15/29,-85/29)\r<BR>\n" );
document.write( "\n" );
document.write( " using determinants\r<BR>\n" );
document.write( "\n" );
document.write( "Summary<BR>\n" );
document.write( "determinant = -29<BR>\n" );
document.write( "a = -480/-29 = 480/29 = 16.5517241<BR>\n" );
document.write( "b = 75/-29 = 75/-29 = -2.5862069<BR>\n" );
document.write( "c = -15/-29 = 15/29 = 0.51724138<BR>\n" );
document.write( "d = 85/-29 = 85/-29 = -2.93103448\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );