document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016590>Question 1016590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x+y+z+w=1<BR>\n" );
document.write( "2x+3z+2w=5<BR>\n" );
document.write( "3x-y+w=-12<BR>\n" );
document.write( "2y+5z+3w=7<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632968 by </B><A HREF=/tutors/aboutme.mpl?userid=FrankM><B>FrankM(1040)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=FrankM><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=FrankM><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=632968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> E1  x+y+z+w=1  <BR>\n" );
document.write( "E2  x+0y+3z+2w=5<BR>\n" );
document.write( "E3  3x-y+0z+w=-12<BR>\n" );
document.write( "E4  0x+2y+5z+3w=7\r<BR>\n" );
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document.write( "4 equations, 4 unknowns. We need to combine 3 pairs of equation to eliminate a variable. Let's start with x. Note, I added the missing variables using 0 as a coefficient. \r<BR>\n" );
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document.write( "-3x+-3y+-3z+-3w=-3  E1*-3<BR>\n" );
document.write( "3x-y+0z+w=-12            E3\r<BR>\n" );
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document.write( "0x-4y-3z-2w=-15   sum1\r<BR>\n" );
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document.write( "-3x+0y-9z-6w=-15  E2*-3<BR>\n" );
document.write( "3x-y+0z+w=-12\r<BR>\n" );
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document.write( "0x-y-9z-5w=-27  sum2\r<BR>\n" );
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document.write( "2y+5z+3w=7  E4 x already gone<BR>\n" );
document.write( "-4y-3z-2w=-15  sum1<BR>\n" );
document.write( "-y-9z-5w=-27  sum2 \r<BR>\n" );
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document.write( "4y+10z+6w=14   E4*2<BR>\n" );
document.write( "-4y-3z-2w=-15   sum1\r<BR>\n" );
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document.write( "0y+7z+4w=-1  sum3\r<BR>\n" );
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document.write( "-4y-36z-20w=-108  sum2*4<BR>\n" );
document.write( "4y+10z+6w=14   E4*2\r<BR>\n" );
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document.write( "0y-26z-14w=-94   sum4\r<BR>\n" );
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document.write( "49z+28w=-7  sum3*7<BR>\n" );
document.write( "-52z-28w=-188   sum4*2\r<BR>\n" );
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document.write( "-3z=-195\r<BR>\n" );
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document.write( "z=65   go to sum 4\r<BR>\n" );
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document.write( "-26(65)-14w=-94\r<BR>\n" );
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document.write( "-1690-14w=-94\r<BR>\n" );
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document.write( "-14w=1596\r<BR>\n" );
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document.write( "w=-114\r<BR>\n" );
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document.write( "x+0y+3z+2w=5  E2 \r<BR>\n" );
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document.write( "x+3(65)+2(-114)=5\r<BR>\n" );
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document.write( "x+195-228=5\r<BR>\n" );
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document.write( "x= 38\r<BR>\n" );
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document.write( "Last, E1\r<BR>\n" );
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document.write( "x+y+z+w=1 \r<BR>\n" );
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document.write( "38+y+65-114=1\r<BR>\n" );
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document.write( "y= 12\r<BR>\n" );
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document.write( "(38,12,65,-114)<BR>\n" );
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