document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059434>Question 1059434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i solve the following 4 x 4 system using elimination & substitution?\r<BR>\n" );
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document.write( "w + 2x + 2y + z  = -2<BR>\n" );
document.write( "w + 3x - 2y - z =  -6<BR>\n" );
document.write( "-2w - x + 3y + 3z =  6<BR>\n" );
document.write( "w + 4x + y - 2z =  -14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674470 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=674470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D ALIGN=MIDDLE  ALT=\"R%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+%2B+2x+%2B+2y+%2B+z++=+-2 ALIGN=MIDDLE  ALT=\"w+%2B+2x+%2B+2y+%2B+z++=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D ALIGN=MIDDLE  ALT=\"R%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+%2B+3x+-+2y+-+z+=++-6 ALIGN=MIDDLE  ALT=\"w+%2B+3x+-+2y+-+z+=++-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B3%5D ALIGN=MIDDLE  ALT=\"R%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2w+-+x+%2B+3y+%2B+3z+=++6 ALIGN=MIDDLE  ALT=\"-2w+-+x+%2B+3y+%2B+3z+=++6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B4%5D ALIGN=MIDDLE  ALT=\"R%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+%2B+4x+%2B+y+-+2z+=++-14 ALIGN=MIDDLE  ALT=\"+w+%2B+4x+%2B+y+-+2z+=++-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate w by using elementary row operations,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D-R%5B2%5D ALIGN=MIDDLE  ALT=\"R%5B1%5D-R%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+%2B+2x+%2B+2y+%2B+z+-w+-+3x+%2B+2y+%2B+z+=-2-%28-6%29 ALIGN=MIDDLE  ALT=\"w+%2B+2x+%2B+2y+%2B+z+-w+-+3x+%2B+2y+%2B+z+=-2-%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D-R%5B2%5D ALIGN=MIDDLE  ALT=\"R%5B1%5D-R%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B4y%2B2z=+4 ALIGN=MIDDLE  ALT=\"-x%2B4y%2B2z=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2R%5B1%5D%2BR%5B3%5D ALIGN=MIDDLE  ALT=\"2R%5B1%5D%2BR%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%2B4x%2B2y%2B2z-2w-x%2B3y%2B3z=-4%2B6 ALIGN=MIDDLE  ALT=\"2w%2B4x%2B2y%2B2z-2w-x%2B3y%2B3z=-4%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2R%5B1%5D%2BR%5B3%5D ALIGN=MIDDLE  ALT=\"2R%5B1%5D%2BR%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B7y%2B5z=2 ALIGN=MIDDLE  ALT=\"3x%2B7y%2B5z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D-R%5B4%5D ALIGN=MIDDLE  ALT=\"R%5B1%5D-R%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+%2B+2x+%2B+2y+%2B+z-w-4x-y%2B2z=-2-%28-14%29 ALIGN=MIDDLE  ALT=\"w+%2B+2x+%2B+2y+%2B+z-w-4x-y%2B2z=-2-%28-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D-R%5B4%5D ALIGN=MIDDLE  ALT=\"R%5B1%5D-R%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By%2B3z=12 ALIGN=MIDDLE  ALT=\"-2x%2By%2B3z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now your reformed equations are,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B5%5D ALIGN=MIDDLE  ALT=\"R%5B5%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B4y%2B2z=+4 ALIGN=MIDDLE  ALT=\"-x%2B4y%2B2z=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B6%5D ALIGN=MIDDLE  ALT=\"R%5B6%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B7y%2B5z=2 ALIGN=MIDDLE  ALT=\"3x%2B7y%2B5z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B7%5D ALIGN=MIDDLE  ALT=\"R%5B7%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By%2B3z=12 ALIGN=MIDDLE  ALT=\"-2x%2By%2B3z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Continue in this fashion until you have solved for one variable and then work backwards. <BR>\n" );
document.write( "You can eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > by these row operations,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3R%5B5%5D%2BR%5B6%5D ALIGN=MIDDLE  ALT=\"3R%5B5%5D%2BR%5B6%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2R%5B5%5D%2BR%5B7%5D ALIGN=MIDDLE  ALT=\"-2R%5B5%5D%2BR%5B7%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );