document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148374>Question 148374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I go about solving a system of equations with three equations and three variables. \r<BR>\n" );
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document.write( "4x-4y-z=38<BR>\n" );
document.write( "x+4y-3z=6<BR>\n" );
document.write( "-3x+2y-z=-14\r<BR>\n" );
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document.write( "Please explain step by step, I would appreciate it. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108942 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=108942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are several methods to choose from. <BR>\n" );
document.write( "One of them is the substitution method. <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4y-z=38 ALIGN=MIDDLE  ALT=\"4x-4y-z=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y-3z=6 ALIGN=MIDDLE  ALT=\"x%2B4y-3z=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B2y-z=-14 ALIGN=MIDDLE  ALT=\"-3x%2B2y-z=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can use eq. 2 to come up with an expression for x in terms of y and z and substitute into eqs. 1 and 3. <BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y-3z=6 ALIGN=MIDDLE  ALT=\"x%2B4y-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=x=-4y%2B3z%2B6 ALIGN=MIDDLE  ALT=\"x=-4y%2B3z%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute into eq. 1,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4y-z=38 ALIGN=MIDDLE  ALT=\"4x-4y-z=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-4y%2B3z%2B6%29-4y-z=38 ALIGN=MIDDLE  ALT=\"4%28-4y%2B3z%2B6%29-4y-z=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16y%2B12z%2B24%29-4y-z=38 ALIGN=MIDDLE  ALT=\"%28-16y%2B12z%2B24%29-4y-z=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20y%2B11z%2B24=38 ALIGN=MIDDLE  ALT=\"-20y%2B11z%2B24=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20y%2B11z=14 ALIGN=MIDDLE  ALT=\"-20y%2B11z=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and eq. 3,<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B2y-z=-14 ALIGN=MIDDLE  ALT=\"-3x%2B2y-z=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%28-4y%2B3z%2B6%29%2B2y-z=-14 ALIGN=MIDDLE  ALT=\"-3%28-4y%2B3z%2B6%29%2B2y-z=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812y-9z-18%29%2B2y-z=-14 ALIGN=MIDDLE  ALT=\"%2812y-9z-18%29%2B2y-z=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14y-10z-18=-14 ALIGN=MIDDLE  ALT=\"14y-10z-18=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14y-10z=4 ALIGN=MIDDLE  ALT=\"14y-10z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y-5z=2 ALIGN=MIDDLE  ALT=\"7y-5z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you've reduce from three variables to two variables. <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20y%2B11z=14 ALIGN=MIDDLE  ALT=\"-20y%2B11z=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y-5z=2 ALIGN=MIDDLE  ALT=\"7y-5z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can again do a substitution to get y in terms of z.<BR>\n" );
document.write( "From new eq. 1,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20y%2B11z=14 ALIGN=MIDDLE  ALT=\"-20y%2B11z=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20y=-11z%2B14 ALIGN=MIDDLE  ALT=\"-20y=-11z%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2811z-14%29%2F20 ALIGN=MIDDLE  ALT=\"y=%2811z-14%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute this value into new eq. 3.<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y-5z=2 ALIGN=MIDDLE  ALT=\"7y-5z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2811z-14%29%2F20%29-5z=2 ALIGN=MIDDLE  ALT=\"%287%2811z-14%29%2F20%29-5z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2811z-14%29%29-100z=40 ALIGN=MIDDLE  ALT=\"%287%2811z-14%29%29-100z=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2877z-98%29-100z=40 ALIGN=MIDDLE  ALT=\"%2877z-98%29-100z=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-23z-98=40 ALIGN=MIDDLE  ALT=\"-23z-98=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-23z=138 ALIGN=MIDDLE  ALT=\"-23z=138\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-6 ALIGN=MIDDLE  ALT=\"z=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now go backwards and substitute to find y and then x.<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y-5z=2 ALIGN=MIDDLE  ALT=\"7y-5z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y-5%28-6%29=2 ALIGN=MIDDLE  ALT=\"7y-5%28-6%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y%2B30=2 ALIGN=MIDDLE  ALT=\"7y%2B30=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=-28 ALIGN=MIDDLE  ALT=\"7y=-28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And finally x,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4y%2B3z%2B6 ALIGN=MIDDLE  ALT=\"x=-4y%2B3z%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%28-4%29%2B3%28-6%29%2B6 ALIGN=MIDDLE  ALT=\"x=-4%28-4%29%2B3%28-6%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16-18%2B6 ALIGN=MIDDLE  ALT=\"x=16-18%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your solution is therefore,<BR>\n" );
document.write( "(x,y,z,)=(4,-4,-6) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );