document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85713>Question 85713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of linear inequalities by graphing.<BR>\n" );
document.write( "	3x – y < 2<BR>\n" );
document.write( "	x + y > 2<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 #61912 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=61912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 12.\r<BR>\n" );
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document.write( "Start with the given system of inequalities\r<BR>\n" );
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document.write( "In order to graph this system of inequalities, we need to graph each inequality one at a time.\r<BR>\n" );
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document.write( "So lets graph the first inequality\r<BR>\n" );
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document.write( "    In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y%3C2 ALIGN=MIDDLE  ALT=\"3x-y%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we need to graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y=2 ALIGN=MIDDLE  ALT=\"3x-y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace the inequality sign with an equal sign). So lets graph the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y=2 ALIGN=MIDDLE  ALT=\"3x-y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%29 ALIGN=MIDDLE  ALT=\"graph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y=2 ALIGN=MIDDLE  ALT=\"3x-y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y%3C2 ALIGN=MIDDLE  ALT=\"3x-y%3C2\"   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=3%280%29-%280%29%3C2 ALIGN=MIDDLE  ALT=\"3%280%29-%280%29%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=0, y=0\r<BR>\n" );
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document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C2 ALIGN=MIDDLE  ALT=\"0%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Since this inequality is true, we shade the entire region containing (0,0)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cgraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B0%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B0.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B1.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B2.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B3%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B3.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B4.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B5.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B6%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B6.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B7.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B8.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B9%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B9.75%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Here is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y%3C2 ALIGN=MIDDLE  ALT=\"3x-y%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the graph of the line(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y=2 ALIGN=MIDDLE  ALT=\"3x-y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) in red and the shaded region in green\r<BR>\n" );
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document.write( "(note: The red line should be a dashed line since it is <b>not</b> included in the region. Since the inequalityis a <font size=6><</font> sign, it tells us <b>not</b> to include the boundaries.)\r<BR>\n" );
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document.write( "Now lets graph the second inequality\r<BR>\n" );
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document.write( "    In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E2 ALIGN=MIDDLE  ALT=\"x%2By%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we need to graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=2 ALIGN=MIDDLE  ALT=\"x%2By=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace the inequality sign with an equal sign). So lets graph the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=2 ALIGN=MIDDLE  ALT=\"x%2By=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%29 ALIGN=MIDDLE  ALT=\"graph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=2 ALIGN=MIDDLE  ALT=\"x%2By=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E2 ALIGN=MIDDLE  ALT=\"x%2By%3E2\"   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=%280%29%2B%280%29%3E2 ALIGN=MIDDLE  ALT=\"%280%29%2B%280%29%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=0, y=0\r<BR>\n" );
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document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E2 ALIGN=MIDDLE  ALT=\"0%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Since this inequality is <b>not</b> true, we shade the entire region that <b>doesn't</b> contain (0,0)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cgraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B0%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B0.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B1.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B2.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B3%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B3.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B4.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B5.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B6%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B6.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B7.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B8.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B9%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B9.75%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Here is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E2 ALIGN=MIDDLE  ALT=\"x%2By%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the graph of the line(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=2 ALIGN=MIDDLE  ALT=\"x%2By=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) in red and the shaded region in green\r<BR>\n" );
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document.write( "(note: The red line should be a dashed line since it is <b>not</b> included in the region. Since the inequalityis a <font size=6>></font> sign, it tells us <b>not</b> to include the boundaries.)\r<BR>\n" );
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document.write( "So we essentially have these 2 regions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cgraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B0%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B0.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B1.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B2.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B3%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B3.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B4.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B5.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B6%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B6.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B7.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B8.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B9%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B9.75%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Region #1 which is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y%3C2 ALIGN=MIDDLE  ALT=\"3x-y%3C2\"   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=drawing%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cgraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B0%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B0.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B1.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B2.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B3%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B3.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B4.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B5.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B6%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B6.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B7.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B8.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B9%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B9.75%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Region #2 which is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E2 ALIGN=MIDDLE  ALT=\"x%2By%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So these regions overlap to produce this region. It's a little hard to see, but after evenly shading each region, the intersecting region will be the most shaded in.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%0D%0Adrawing%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B0%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B0.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B1.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B2.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B3%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B3.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B4.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B5.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B6%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B6.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B7.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B8.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B9%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C+%282-3%2Ax%29%2F-1%2B9.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B0%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B0.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B1.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B2.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B3%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B3.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B4.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B5.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B6%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B6.75%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B7.5%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B8.25%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B9%29%2C%0D%0Agraph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-1%2Ax%29%2F1%2C+%282-1%2Ax%29%2F1%2B9.75%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Here is a cleaner look at the intersection of regions\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++graph%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282-3%2Ax%29%2F-1%2C%282-1%2Ax%29%2F1%29%2Ccircle%28-6.5%2C9.25%2C0.05%29%2C%0D%0A+circle%28-6.5%2C9.25%2C0.08%29%2Ccircle%28-4.75%2C7.5%2C0.05%29%2C%0D%0A+circle%28-4.75%2C7.5%2C0.08%29%2Ccircle%28-4.75%2C9.25%2C0.05%29%2C%0D%0A+circle%28-4.75%2C9.25%2C0.08%29%2Ccircle%28-3%2C5.75%2C0.05%29%2C%0D%0A+circle%28-3%2C5.75%2C0.08%29%2Ccircle%28-3%2C7.5%2C0.05%29%2C%0D%0A+circle%28-3%2C7.5%2C0.08%29%2Ccircle%28-3%2C9.25%2C0.05%29%2C%0D%0A+circle%28-3%2C9.25%2C0.08%29%2Ccircle%28-1.25%2C4%2C0.05%29%2C%0D%0A+circle%28-1.25%2C4%2C0.08%29%2Ccircle%28-1.25%2C5.75%2C0.05%29%2C%0D%0A+circle%28-1.25%2C5.75%2C0.08%29%2Ccircle%28-1.25%2C7.5%2C0.05%29%2C%0D%0A+circle%28-1.25%2C7.5%2C0.08%29%2Ccircle%28-1.25%2C9.25%2C0.05%29%2C%0D%0A+circle%28-1.25%2C9.25%2C0.08%29%2Ccircle%280.5%2C2.25%2C0.05%29%2C%0D%0A+circle%280.5%2C2.25%2C0.08%29%2Ccircle%280.5%2C4%2C0.05%29%2C%0D%0A+circle%280.5%2C4%2C0.08%29%2Ccircle%280.5%2C5.75%2C0.05%29%2C%0D%0A+circle%280.5%2C5.75%2C0.08%29%2Ccircle%280.5%2C7.5%2C0.05%29%2C%0D%0A+circle%280.5%2C7.5%2C0.08%29%2Ccircle%280.5%2C9.25%2C0.05%29%2C%0D%0A+circle%280.5%2C9.25%2C0.08%29%2Ccircle%282.25%2C5.75%2C0.05%29%2C%0D%0A+circle%282.25%2C5.75%2C0.08%29%2Ccircle%282.25%2C7.5%2C0.05%29%2C%0D%0A+circle%282.25%2C7.5%2C0.08%29%2Ccircle%282.25%2C9.25%2C0.05%29%2C%0D%0A+circle%282.25%2C9.25%2C0.08%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Here is the intersection of the 2 regions represented by the dots </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );