document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44751>Question 44751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> equations with 3 linear variables\r<BR>\n" );
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document.write( "6x-4y+5z=31<BR>\n" );
document.write( "5x+2y+2z=13<BR>\n" );
document.write( "x+y+z=2\r<BR>\n" );
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document.write( "should you multiply the 2nd equation by 2?\r<BR>\n" );
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document.write( "show work </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29601 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=29601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK..THE PROBLEM,WE FACE IN ANSWERING IS THAT WE ARE NOT AWARE OF YOUR COURSE OF STUDY AND BACKGROUND.THE SOLUTION I GAVE IS BY GAUSS JORDAN ELIMINATION METHOD USED IN MATRICES AS WANTED BY SOME STUDENTS.IF YOU ARE NOT TAUGHT THAT ,WE SHALL DO BY NORMAL ELIMINATION.\r<BR>\n" );
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document.write( "equations with 3 linear variables<BR>\n" );
document.write( "6x-4y+5z=31.......................................I<BR>\n" );
document.write( "5x+2y+2z=13...........................II<BR>\n" );
document.write( "x+y+z=2.......................III<BR>\n" );
document.write( "EQN.II - 2*EQN.III<BR>\n" );
document.write( "5X+2Y+2Z-2X-2Y-2Z=13-2*2=9<BR>\n" );
document.write( "3X=9<BR>\n" );
document.write( "X=9/3=3<BR>\n" );
document.write( "EQN.I+4*EQN.III<BR>\n" );
document.write( "6X-4Y+5Z+4X+4Y+4Z=31+4*2=39<BR>\n" );
document.write( "10X+9Z=39...BUT...X=3..SO<BR>\n" );
document.write( "10*3+9Z=39<BR>\n" );
document.write( "9Z=39-30=9<BR>\n" );
document.write( "Z=9/9=1<BR>\n" );
document.write( "PUTTING IN EQN.III<BR>\n" );
document.write( "3+Y+1=2<BR>\n" );
document.write( "Y=2-4=-2<BR>\n" );
document.write( "HOPE YOU UNDERSTOOD.<BR>\n" );
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document.write( "SEE THE FOLLOWING AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK<BR>\n" );
document.write( "YOU MAY MULTIPLY EQN.II WITH 2 AND ADD TO EQN.I TO ELIMINATE Y<BR>\n" );
document.write( "x - y + z = 2<BR>\n" );
document.write( "-x + y + z = 4<BR>\n" );
document.write( "-x + z = 2<BR>\n" );
document.write( "augmented matrix is<BR>\n" );
document.write( "1.....................-1.......................1.............................2<BR>\n" );
document.write( "-1.....................1.......................1.............................4<BR>\n" );
document.write( "-1.....................0.......................1.............................2<BR>\n" );
document.write( "nr2=r2+r1 and nr3=r3+r1<BR>\n" );
document.write( "1..................-1.................1.............2<BR>\n" );
document.write( "1-1=0............1-1=0............1+1=2..........2+4=6<BR>\n" );
document.write( "1-1=0...........-1+0=-1...........1+1=2..........2+2=4<BR>\n" );
document.write( "nr2=r2/2....nr3=r3-r2<BR>\n" );
document.write( "1....................-1...............1..............2<BR>\n" );
document.write( "0/2=0.............0/2=0..............2/2=1........6/2=3<BR>\n" );
document.write( "0-0=0............-1-0=-1..............2-2=0.......4-6=-2<BR>\n" );
document.write( "nr1=r1-r3-r2.......nr2=2r2........nr3=-r3<BR>\n" );
document.write( "1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1<BR>\n" );
document.write( "0.....................0...................1............3<BR>\n" );
document.write( "0.....................1...................0.............2<BR>\n" );
document.write( "exchange r2 and r3<BR>\n" );
document.write( "1....0........0.......1<BR>\n" );
document.write( "0....1........0.......2<BR>\n" );
document.write( "0....0........1.......3<BR>\n" );
document.write( "he\r<BR>\n" );
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document.write( "nce x=1......y=2.....z=3  </SPAN>\n" );
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