document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175220>Question 1175220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the solution to the system of equations:\r<BR>\n" );
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document.write( "(x - 2y + z = -3<BR>\n" );
document.write( "|y + 2z = -5<BR>\n" );
document.write( "|x + y + 3z = -6<BR>\n" );
document.write( "(\r<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 #800795 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=800795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are many methods -- elimination, Cramer's rule, matrices with Gauss-Jordan....<br><BR>\n" );
document.write( "Using Cramer's rule is a well-defined process; if you want to solve the problem that way, just do it.<br><BR>\n" );
document.write( "Using Gauss-Jordan elimination is also a well-defined process, but there are multiple possible paths to the solution, and the process is prone to simple arithmetic errors.<br><BR>\n" );
document.write( "Given no instruction on what method to use, I would solve the problem algebraically using elimination.<br><BR>\n" );
document.write( "Since one of the equations involves only two of the three variables, I would solve that equation for one variable in terms of the other and then use substitution to reduce the problem to two equations in two unknowns.<br><BR>\n" );
document.write( "Presumably if you are working on a problem like this you know how to solve a system of two linear equations; so I leave the last part of the work to you.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2z+=+-5 ALIGN=MIDDLE  ALT=\"y%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=y+=+-5-2z ALIGN=MIDDLE  ALT=\"y+=+-5-2z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%28-5-2z%29%2Bz+=+-3 ALIGN=MIDDLE  ALT=\"x-2%28-5-2z%29%2Bz+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5z+=+-13 ALIGN=MIDDLE  ALT=\"x%2B5z+=+-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1]<br><BR>\n" );
document.write( "and<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B%28-5-2z%29%2B3z+=+-6 ALIGN=MIDDLE  ALT=\"x%2B%28-5-2z%29%2B3z+=+-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%2Bz+=+-1 ALIGN=MIDDLE  ALT=\"x%2Bz+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<br><BR>\n" );
document.write( "Solve [1] and [2] for x and z; then find y from one of the given equations.<br><BR>\n" );
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