document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146537>Question 146537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!\r<BR>\n" );
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document.write( "Tell whether the given ordered triple is a solution of the system.\r<BR>\n" );
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document.write( "1) (5, -2, 2)<BR>\n" );
document.write( "2x-y+z=5<BR>\n" );
document.write( "x+2y-z=-1<BR>\n" );
document.write( "-2x+y-3z=-15\r<BR>\n" );
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document.write( "2) (1, -1, 3)<BR>\n" );
document.write( "4x+2y+3z=11<BR>\n" );
document.write( "x-2y+z=6<BR>\n" );
document.write( "2x+y+2z=7\r<BR>\n" );
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document.write( "Thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106973 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=106973\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)\r<BR>\n" );
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document.write( "------------------ Let's test the first equation ------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y%2Bz=5 ALIGN=MIDDLE  ALT=\"2x-y%2Bz=5\"   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=2%2A%285%29-%28-2%29%2B%282%29=5 ALIGN=MIDDLE  ALT=\"2%2A%285%29-%28-2%29%2B%282%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   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=2 ALIGN=MIDDLE  ALT=\"z=2\"   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=14=5 ALIGN=MIDDLE  ALT=\"14=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side.\r<BR>\n" );
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document.write( "Since the equation is <b>not</b> true, this means that (5, -2, 2) is <b>not</b> a solution to the system. Remember, a solution has to satisfy <b>all</b> of the equations in the system.\r<BR>\n" );
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document.write( "2)\r<BR>\n" );
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document.write( "------------------ Let's test 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%2B2y%2B3z=11 ALIGN=MIDDLE  ALT=\"4x%2B2y%2B3z=11\"   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=4%2A%281%29%2B2%2A%28-1%29%2B3%2A%283%29=11 ALIGN=MIDDLE  ALT=\"4%2A%281%29%2B2%2A%28-1%29%2B3%2A%283%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=3 ALIGN=MIDDLE  ALT=\"z=3\"   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=11=11 ALIGN=MIDDLE  ALT=\"11=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side.\r<BR>\n" );
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document.write( "Notice how the equation is true.\r<BR>\n" );
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document.write( "------------------ Now let's test the second equation ------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y%2Bz=6 ALIGN=MIDDLE  ALT=\"x-2y%2Bz=6\"   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=%281%29-2%2A%28-1%29%2B%283%29=6 ALIGN=MIDDLE  ALT=\"%281%29-2%2A%28-1%29%2B%283%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=3 ALIGN=MIDDLE  ALT=\"z=3\"   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=6=6 ALIGN=MIDDLE  ALT=\"6=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side.\r<BR>\n" );
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document.write( "Notice how the equation is true.\r<BR>\n" );
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document.write( "------------------ Now let's test the third equation ------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%2B2z=7 ALIGN=MIDDLE  ALT=\"2x%2By%2B2z=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the third equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%281%29%2B%28-1%29%2B2%2A%283%29=7 ALIGN=MIDDLE  ALT=\"2%2A%281%29%2B%28-1%29%2B2%2A%283%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=3 ALIGN=MIDDLE  ALT=\"z=3\"   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=7=7 ALIGN=MIDDLE  ALT=\"7=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side.\r<BR>\n" );
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document.write( "Notice how the equation is true.\r<BR>\n" );
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document.write( "Since <b>all</b> of the equations in the system are true, this means that (1, -1, 3) is a solution. </SPAN>\n" );
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