document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172787>Question 172787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve\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 #127628 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=127628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x-y%2B2z=-3%2C+x%2B2y%2B3z=4%2C+2x%2By%2Bz=-3%29 ALIGN=MIDDLE  ALT=\"system%28x-y%2B2z=-3%2C+x%2B2y%2B3z=4%2C+2x%2By%2Bz=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%2B2z=-3 ALIGN=MIDDLE  ALT=\"x-y%2B2z=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2By-2z ALIGN=MIDDLE  ALT=\"x=-3%2By-2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add \"y\" to both sides. Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z ALIGN=MIDDLE  ALT=\"2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. Now let's call this equation 4.\r<BR>\n" );
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document.write( "-------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%2Bz=-3 ALIGN=MIDDLE  ALT=\"2x%2By%2Bz=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the third equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3-2x-z ALIGN=MIDDLE  ALT=\"y=-3-2x-z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides. Subtract \"z\" from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3-2%28-3%2By-2z%29-z ALIGN=MIDDLE  ALT=\"y=-3-2%28-3%2By-2z%29-z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2By-2z ALIGN=MIDDLE  ALT=\"x=-3%2By-2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > (equation 4).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2B6-2y%2B4z-z ALIGN=MIDDLE  ALT=\"y=-3%2B6-2y%2B4z-z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-2y%2B3z ALIGN=MIDDLE  ALT=\"y=3-2y%2B3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2y=3%2B3z ALIGN=MIDDLE  ALT=\"y%2B2y=3%2B3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2y to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=3%2B3z ALIGN=MIDDLE  ALT=\"3y=3%2B3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2B3z%29%2F3 ALIGN=MIDDLE  ALT=\"y=%283%2B3z%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to isolate \"y\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%29%2F3%2B%283z%29%2F3 ALIGN=MIDDLE  ALT=\"y=%283%29%2F3%2B%283z%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Bz ALIGN=MIDDLE  ALT=\"y=1%2Bz\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z%2B1 ALIGN=MIDDLE  ALT=\"y=z%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms. Let's call this equation 5.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y%2B3z=4 ALIGN=MIDDLE  ALT=\"x%2B2y%2B3z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2By-2z%29%2B2%28z%2B1%29%2B3z=4 ALIGN=MIDDLE  ALT=\"%28-3%2By-2z%29%2B2%28z%2B1%29%2B3z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2By-2z ALIGN=MIDDLE  ALT=\"x=-3%2By-2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > (equation 4) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z%2B1 ALIGN=MIDDLE  ALT=\"y=z%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (equation 5)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2By-2z%2B2z%2B2%2B3z=4 ALIGN=MIDDLE  ALT=\"-3%2By-2z%2B2z%2B2%2B3z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2By%2B3z=4 ALIGN=MIDDLE  ALT=\"-1%2By%2B3z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3z=4%2B1 ALIGN=MIDDLE  ALT=\"y%2B3z=4%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3z=5 ALIGN=MIDDLE  ALT=\"y%2B3z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add. Now let's call this equation 6. \r<BR>\n" );
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document.write( "Are you with me so far? Well after all that substitution and simplification, we have the equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2By-2z ALIGN=MIDDLE  ALT=\"x=-3%2By-2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z%2B1 ALIGN=MIDDLE  ALT=\"y=z%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3z=5 ALIGN=MIDDLE  ALT=\"y%2B3z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation 6\r<BR>\n" );
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document.write( "So let's solve the system of equations of 5 and 6  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3z=5 ALIGN=MIDDLE  ALT=\"y%2B3z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with equation 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2B1%2B3z=5 ALIGN=MIDDLE  ALT=\"z%2B1%2B3z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z%2B1 ALIGN=MIDDLE  ALT=\"y=z%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Equation 5).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4z=5 ALIGN=MIDDLE  ALT=\"1%2B4z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4z=5-1 ALIGN=MIDDLE  ALT=\"4z=5-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4z=4 ALIGN=MIDDLE  ALT=\"4z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%284%29%2F%284%29 ALIGN=MIDDLE  ALT=\"z=%284%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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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;\" > Reduce. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z%2B1 ALIGN=MIDDLE  ALT=\"y=z%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to Equation 5.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2By-2z ALIGN=MIDDLE  ALT=\"x=-3%2By-2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to equation 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2B2-2%281%29 ALIGN=MIDDLE  ALT=\"x=-3%2B2-2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <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;\" >\r<BR>\n" );
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document.write( "These solutions form the ordered triple (-3,2,1)\r<BR>\n" );
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