document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6156>Question 6156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The whole third variable thing confuses me. When I try and do it by substitution I always end up with this long chain that I don't know how to reduce to find the answer for the second variable. Thanks in advance.\r<BR>\n" );
document.write( "\n" );
document.write( "Solve for X, Y and Z<BR>\n" );
document.write( "22X + 5Y + 7Z = 12<BR>\n" );
document.write( "10X + 3Y + 2Z = 5<BR>\n" );
document.write( "9X  +  2Y +  12Z = 14 <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3278 by </B><A HREF=/tutors/aboutme.mpl?userid=glabow><B>glabow(165)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=glabow><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are looking to find one variable in terms of the others. You do this by rearranging. Rearrange the last equation to find y. (I picked that one because it looked good. Any others will work too.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x+%2B+2y%2B12z=14 ALIGN=MIDDLE  ALT=\"9x+%2B+2y%2B12z=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > rearranges to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=14-12z-9x ALIGN=MIDDLE  ALT=\"2y=14-12z-9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2814-12z-9x%29%2F2 ALIGN=MIDDLE  ALT=\"y=%2814-12z-9x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute this value for y in the equations. The first looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22x%2B%285%2814-12z-9x%29%2F2%29%2B7z=12 ALIGN=MIDDLE  ALT=\"22x%2B%285%2814-12z-9x%29%2F2%29%2B7z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22x%2B%28%2870-60z-45x%29%2F2%29%2B7z=12 ALIGN=MIDDLE  ALT=\"22x%2B%28%2870-60z-45x%29%2F2%29%2B7z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44x%2B70-60z-45x%2B14z=24 ALIGN=MIDDLE  ALT=\"44x%2B70-60z-45x%2B14z=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-46z=-46 ALIGN=MIDDLE  ALT=\"-x-46z=-46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B46z=46 ALIGN=MIDDLE  ALT=\"x+%2B46z=46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Do the same substitution with the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B%283%2814-12z-9x%29%2F2%29%2B2z=5 ALIGN=MIDDLE  ALT=\"10x%2B%283%2814-12z-9x%29%2F2%29%2B2z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B%28%2842-36z-27x%29%2F2%29%2B2z=5 ALIGN=MIDDLE  ALT=\"10x%2B%28%2842-36z-27x%29%2F2%29%2B2z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%2B42-36z-27x%2B4z=10 ALIGN=MIDDLE  ALT=\"20x%2B42-36z-27x%2B4z=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x-32z=-32 ALIGN=MIDDLE  ALT=\"-7x-32z=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B32z=32 ALIGN=MIDDLE  ALT=\"7x%2B32z=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now do the same elimination with the two equations in x and z.<BR>\n" );
document.write( "The first equation says<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=46-46z ALIGN=MIDDLE  ALT=\"x=46-46z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute x in the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2846-46z%29%2B32z=32 ALIGN=MIDDLE  ALT=\"7%2846-46z%29%2B32z=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=322-322z%2B32z=32 ALIGN=MIDDLE  ALT=\"322-322z%2B32z=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [resist the urge to simplify!]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-322z%2B32z=32-322 ALIGN=MIDDLE  ALT=\"-322z%2B32z=32-322\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32z-322z=32-322 ALIGN=MIDDLE  ALT=\"32z-322z=32-322\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832-322%29z=%2832-322%29 ALIGN=MIDDLE  ALT=\"%2832-322%29z=%2832-322%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [factor out 32-322]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=1 ALIGN=MIDDLE  ALT=\"z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [divide by (32-322) !]<BR>\n" );
document.write( "Now substitute the value for z in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=46-46z ALIGN=MIDDLE  ALT=\"x=46-46z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute the values for x and z in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2B2y%2B12z=14 ALIGN=MIDDLE  ALT=\"9x%2B2y%2B12z=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=14-0-12 ALIGN=MIDDLE  ALT=\"2y=14-0-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check in the original equations.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );