document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253952>Question 253952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x+y-2z=0<BR>\n" );
document.write( "3x+y=1<BR>\n" );
document.write( "5x+3y+7z=2\r<BR>\n" );
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document.write( "x=<BR>\n" );
document.write( "y=<BR>\n" );
document.write( "z= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186316 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=186316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By=1 ALIGN=MIDDLE  ALT=\"3x%2By=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B1 ALIGN=MIDDLE  ALT=\"y=-3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3x from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By-2z=0 ALIGN=MIDDLE  ALT=\"x%2By-2z=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move back to 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-3x%2B1-2z=0 ALIGN=MIDDLE  ALT=\"x-3x%2B1-2z=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B1 ALIGN=MIDDLE  ALT=\"y=-3x%2B1\"   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=-2x%2B1-2z=0 ALIGN=MIDDLE  ALT=\"-2x%2B1-2z=0\"   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=-2x-2z=-1 ALIGN=MIDDLE  ALT=\"-2x-2z=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2z=1 ALIGN=MIDDLE  ALT=\"2x%2B2z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply every term by -1\r<BR>\n" );
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document.write( "So let's make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2z=1 ALIGN=MIDDLE  ALT=\"2x%2B2z=1\"   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=5x%2B3y%2B7z=2 ALIGN=MIDDLE  ALT=\"5x%2B3y%2B7z=2\"   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=5x%2B3%28-3x%2B1%29%2B7z=2 ALIGN=MIDDLE  ALT=\"5x%2B3%28-3x%2B1%29%2B7z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B1 ALIGN=MIDDLE  ALT=\"y=-3x%2B1\"   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=5x-9x%2B3%2B7z=2 ALIGN=MIDDLE  ALT=\"5x-9x%2B3%2B7z=2\"   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=-4x-3%2B7z=2 ALIGN=MIDDLE  ALT=\"-4x-3%2B7z=2\"   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=-4x%2B7z=2-3 ALIGN=MIDDLE  ALT=\"-4x%2B7z=2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%2B7z=-1 ALIGN=MIDDLE  ALT=\"-4x%2B7z=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. We'll make this equation 5.\r<BR>\n" );
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document.write( "So we have the new 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%282x%2B2z=1%2C-4x%2B7z=-1%29 ALIGN=MIDDLE  ALT=\"system%282x%2B2z=1%2C-4x%2B7z=-1%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=2%282x%2B2z%29=2%281%29 ALIGN=MIDDLE  ALT=\"2%282x%2B2z%29=2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B4z=2 ALIGN=MIDDLE  ALT=\"4x%2B4z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we now have\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B4z%29%2B%28-4x%2B7z%29=%282%29%2B%28-1%29 ALIGN=MIDDLE  ALT=\"%284x%2B4z%29%2B%28-4x%2B7z%29=%282%29%2B%28-1%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=%284x%2B-4x%29%2B%284z%2B7z%29=2%2B-1 ALIGN=MIDDLE  ALT=\"%284x%2B-4x%29%2B%284z%2B7z%29=2%2B-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B11z=1 ALIGN=MIDDLE  ALT=\"0x%2B11z=1\"   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=11z=1 ALIGN=MIDDLE  ALT=\"11z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%281%29%2F%2811%29 ALIGN=MIDDLE  ALT=\"z=%281%29%2F%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   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=4x%2B4z=2 ALIGN=MIDDLE  ALT=\"4x%2B4z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B4%281%2F11%29=2 ALIGN=MIDDLE  ALT=\"4x%2B4%281%2F11%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=1%2F11 ALIGN=MIDDLE  ALT=\"z=1%2F11\"   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=4x%2B4%2F11=2 ALIGN=MIDDLE  ALT=\"4x%2B4%2F11=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%284x%2B4%2Fcross%2811%29%29=11%282%29 ALIGN=MIDDLE  ALT=\"11%284x%2B4%2Fcross%2811%29%29=11%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44x%2B4=22 ALIGN=MIDDLE  ALT=\"44x%2B4=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44x=22-4 ALIGN=MIDDLE  ALT=\"44x=22-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=44x=18 ALIGN=MIDDLE  ALT=\"44x=18\"   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=x=%2818%29%2F%2844%29 ALIGN=MIDDLE  ALT=\"x=%2818%29%2F%2844%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=9%2F22 ALIGN=MIDDLE  ALT=\"x=9%2F22\"   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=-3x%2B1 ALIGN=MIDDLE  ALT=\"y=-3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the previously isolated equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%289%2F22%29%2B1 ALIGN=MIDDLE  ALT=\"y=-3%289%2F22%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9%2F22 ALIGN=MIDDLE  ALT=\"x=9%2F22\"   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=y=-5%2F22 ALIGN=MIDDLE  ALT=\"y=-5%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\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=9%2F22 ALIGN=MIDDLE  ALT=\"x=9%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%2F22 ALIGN=MIDDLE  ALT=\"y=-5%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=1%2F11 ALIGN=MIDDLE  ALT=\"z=1%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Which form the ordered triple <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{9}{22},-\frac{5}{22}, \frac{1}{11}\right)\">.\r<BR>\n" );
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document.write( "This means that the system is consistent and independent. </SPAN>\n" );
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