document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203437>Question 1203437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x+6y-z=7<BR>\n" );
document.write( "2x-3y+5z=-12<BR>\n" );
document.write( "8x+9y-2z=12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839011 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The button on wolframalpha.com for seeing the step-by-step solution does not work unless you have acquired special privileges on their site.  And the beginning of the step-by-step solution you can see shows a rigid solution method that might not be the easiest.<br><BR>\n" );
document.write( "And with a system of 3 equations I would not use substitution as the other tutor does... although that is a valid method.<br><BR>\n" );
document.write( "Given three linear equations in three variables, I would definitely use elimination instead of substitution.<br><BR>\n" );
document.write( "The general solution method for a system of any number of linear equations is to eliminate one variable at a time.<br><BR>\n" );
document.write( "Our equations are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B6y-z=7 ALIGN=MIDDLE  ALT=\"3x%2B6y-z=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%2B5z=-12 ALIGN=MIDDLE  ALT=\"2x-3y%2B5z=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B9y-2z=12 ALIGN=MIDDLE  ALT=\"8x%2B9y-2z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [3]<br><BR>\n" );
document.write( "Use the \"-z\" in the first equation to eliminate the variable z in the other two equations, using elimination.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%2B30y-5z=35 ALIGN=MIDDLE  ALT=\"15x%2B30y-5z=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1], multiplied by 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%2B5z=-12 ALIGN=MIDDLE  ALT=\"2x-3y%2B5z=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x%2B27y=23 ALIGN=MIDDLE  ALT=\"17x%2B27y=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [4] [the sum of those two equations]<br><BR>\n" );
document.write( "and<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-12y%2B2z=-14 ALIGN=MIDDLE  ALT=\"-6x-12y%2B2z=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1], multiplied by -2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B9y-2z=12 ALIGN=MIDDLE  ALT=\"8x%2B9y-2z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=-2 ALIGN=MIDDLE  ALT=\"2x-3y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [5] [the sum of those two equations]<br><BR>\n" );
document.write( "We have reduced the system of 3 equations in 3 variables to a system of 2 equations in 2 variables.  Use elimination again to eliminate one of the variables; solve for the remaining variable, and back substitute to find the final answer.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x%2B27y=23 ALIGN=MIDDLE  ALT=\"17x%2B27y=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [4]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-27y=-18 ALIGN=MIDDLE  ALT=\"18x-27y=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [5], multiplied by 9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35x=5 ALIGN=MIDDLE  ALT=\"35x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [the sum of those two equations]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F35+=+1%2F7 ALIGN=MIDDLE  ALT=\"x=5%2F35+=+1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute x = 1/7 in [5] and solve for y<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F7-3y=-2 ALIGN=MIDDLE  ALT=\"2%2F7-3y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-21y=-14 ALIGN=MIDDLE  ALT=\"2-21y=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21y=-16 ALIGN=MIDDLE  ALT=\"-21y=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-16%29%2F%28-21%29=16%2F21 ALIGN=MIDDLE  ALT=\"y=%28-16%29%2F%28-21%29=16%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute x = 1/7 and y = 16/21 in [1] and solve for z<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7%2B6%2816%2F21%29-z=7 ALIGN=MIDDLE  ALT=\"3%2F7%2B6%2816%2F21%29-z=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7%2B32%2F7-z=7 ALIGN=MIDDLE  ALT=\"3%2F7%2B32%2F7-z=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F7-z=7 ALIGN=MIDDLE  ALT=\"35%2F7-z=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-z=7 ALIGN=MIDDLE  ALT=\"5-z=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2 ALIGN=MIDDLE  ALT=\"z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: (x,y,z) = (1/7,16/21,-2)<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );