document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198852>Question 198852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My work sheet says \"Systems of Linear Inequalities\" so hopefully somoene can help... IDK how to graph this or wat to even do... can you help me?\r<BR>\n" );
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document.write( "y > 2x +3 ( the > is equal to or greater than)<BR>\n" );
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document.write( "y < 1\r<BR>\n" );
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document.write( "And it says somethin about the dark portion of the graph is the answer.... \r<BR>\n" );
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document.write( "I am no tlooking fo rthe answer but just a way that I can understyand in the 8th grade<BR>\n" );
document.write( "THANKZ!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149338 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=149338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given system of inequalities\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y%3E2x%2B3%2Cy%3C1%29 ALIGN=MIDDLE  ALT=\"system%28y%3E2x%2B3%2Cy%3C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "First lets graph the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E2x%2B3 ALIGN=MIDDLE  ALT=\"y%3E2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=y%3E2x%2B3 ALIGN=MIDDLE  ALT=\"y%3E2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to graph the <b>equation</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace the inequality sign with an equal sign).<BR>\n" );
document.write( "So lets graph the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%2B3\"   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+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+2x%2B3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+2x%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%2B3\"   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, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By%3E3 ALIGN=MIDDLE  ALT=\"-2x%2By%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the test point\r<BR>\n" );
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document.write( "Substitute (0,0) into the inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E2x%2B3 ALIGN=MIDDLE  ALT=\"y%3E2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E2%280%29%2B3 ALIGN=MIDDLE  ALT=\"0%3E2%280%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   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=0%3E0%2B3 ALIGN=MIDDLE  ALT=\"0%3E0%2B3\"   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=0%3E3 ALIGN=MIDDLE  ALT=\"0%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Since this inequality is <font size=4><b>not</b></font> true, we do <font size=4><b>not</b></font> shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B3%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B9%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B15%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B21%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B27%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B30%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B33%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B39%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B42%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B45%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B48%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E2x%2B3 ALIGN=MIDDLE  ALT=\"y%3E2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the boundary (which is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > in red) and the shaded region (in green) <BR>\n" );
document.write( "(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)\r<BR>\n" );
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document.write( "Now lets graph the second inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C1 ALIGN=MIDDLE  ALT=\"y%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=y%3C1 ALIGN=MIDDLE  ALT=\"y%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to graph the <b>equation</b> <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;\" > (just replace the inequality sign with an equal sign).<BR>\n" );
document.write( "So lets graph the line <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;\" > (simply draw a horizontal line through <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;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <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;\" > \r<BR>\n" );
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document.write( "Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C1 ALIGN=MIDDLE  ALT=\"y%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the test point\r<BR>\n" );
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document.write( "Substitute (0,0) into the inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29%3C1 ALIGN=MIDDLE  ALT=\"%280%29%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   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=0%3C1 ALIGN=MIDDLE  ALT=\"0%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Since this inequality is true, we simply shade the entire region that contains (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+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-3%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-9%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-15%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-21%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-27%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-30%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-33%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-39%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-42%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-45%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-48%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C1 ALIGN=MIDDLE  ALT=\"y%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the boundary (which is the line <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;\" > in red) and the shaded region (in green) <BR>\n" );
document.write( "(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)\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( "Region #1<BR>\n" );
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document.write( "Region #2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-48%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C1 ALIGN=MIDDLE  ALT=\"y%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When these inequalities are graphed on the same coordinate system, the 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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C2x%2B3%2B48%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C1%2C1%2B-48%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is a cleaner look at the intersection of regions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0A++++++++++graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C2x%2B3%2C1%29%2Ccircle%28-20%2C-20%2C0.2%29%2C%0D%0Acircle%28-20%2C-17%2C0.2%29%2C%0D%0Acircle%28-20%2C-14%2C0.2%29%2C%0D%0Acircle%28-20%2C-11%2C0.2%29%2C%0D%0Acircle%28-20%2C-8%2C0.2%29%2C%0D%0Acircle%28-20%2C-5%2C0.2%29%2C%0D%0Acircle%28-20%2C-2%2C0.2%29%2C%0D%0Acircle%28-17%2C-20%2C0.2%29%2C%0D%0Acircle%28-17%2C-17%2C0.2%29%2C%0D%0Acircle%28-17%2C-14%2C0.2%29%2C%0D%0Acircle%28-17%2C-11%2C0.2%29%2C%0D%0Acircle%28-17%2C-8%2C0.2%29%2C%0D%0Acircle%28-17%2C-5%2C0.2%29%2C%0D%0Acircle%28-17%2C-2%2C0.2%29%2C%0D%0Acircle%28-14%2C-20%2C0.2%29%2C%0D%0Acircle%28-14%2C-17%2C0.2%29%2C%0D%0Acircle%28-14%2C-14%2C0.2%29%2C%0D%0Acircle%28-14%2C-11%2C0.2%29%2C%0D%0Acircle%28-14%2C-8%2C0.2%29%2C%0D%0Acircle%28-14%2C-5%2C0.2%29%2C%0D%0Acircle%28-14%2C-2%2C0.2%29%2C%0D%0Acircle%28-11%2C-17%2C0.2%29%2C%0D%0Acircle%28-11%2C-14%2C0.2%29%2C%0D%0Acircle%28-11%2C-11%2C0.2%29%2C%0D%0Acircle%28-11%2C-8%2C0.2%29%2C%0D%0Acircle%28-11%2C-5%2C0.2%29%2C%0D%0Acircle%28-11%2C-2%2C0.2%29%2C%0D%0Acircle%28-8%2C-11%2C0.2%29%2C%0D%0Acircle%28-8%2C-8%2C0.2%29%2C%0D%0Acircle%28-8%2C-5%2C0.2%29%2C%0D%0Acircle%28-8%2C-2%2C0.2%29%2C%0D%0Acircle%28-5%2C-5%2C0.2%29%2C%0D%0Acircle%28-5%2C-2%2C0.2%29%2C%0D%0Acircle%28-20%2C-20%2C0.2%29%2C%0D%0Acircle%28-20%2C-17%2C0.2%29%2C%0D%0Acircle%28-20%2C-14%2C0.2%29%2C%0D%0Acircle%28-20%2C-11%2C0.2%29%2C%0D%0Acircle%28-20%2C-8%2C0.2%29%2C%0D%0Acircle%28-20%2C-5%2C0.2%29%2C%0D%0Acircle%28-20%2C-2%2C0.2%29%2C%0D%0Acircle%28-17%2C-20%2C0.2%29%2C%0D%0Acircle%28-17%2C-17%2C0.2%29%2C%0D%0Acircle%28-17%2C-14%2C0.2%29%2C%0D%0Acircle%28-17%2C-11%2C0.2%29%2C%0D%0Acircle%28-17%2C-8%2C0.2%29%2C%0D%0Acircle%28-17%2C-5%2C0.2%29%2C%0D%0Acircle%28-17%2C-2%2C0.2%29%2C%0D%0Acircle%28-14%2C-20%2C0.2%29%2C%0D%0Acircle%28-14%2C-17%2C0.2%29%2C%0D%0Acircle%28-14%2C-14%2C0.2%29%2C%0D%0Acircle%28-14%2C-11%2C0.2%29%2C%0D%0Acircle%28-14%2C-8%2C0.2%29%2C%0D%0Acircle%28-14%2C-5%2C0.2%29%2C%0D%0Acircle%28-14%2C-2%2C0.2%29%2C%0D%0Acircle%28-11%2C-17%2C0.2%29%2C%0D%0Acircle%28-11%2C-14%2C0.2%29%2C%0D%0Acircle%28-11%2C-11%2C0.2%29%2C%0D%0Acircle%28-11%2C-8%2C0.2%29%2C%0D%0Acircle%28-11%2C-5%2C0.2%29%2C%0D%0Acircle%28-11%2C-2%2C0.2%29%2C%0D%0Acircle%28-8%2C-11%2C0.2%29%2C%0D%0Acircle%28-8%2C-8%2C0.2%29%2C%0D%0Acircle%28-8%2C-5%2C0.2%29%2C%0D%0Acircle%28-8%2C-2%2C0.2%29%2C%0D%0Acircle%28-5%2C-5%2C0.2%29%2C%0D%0Acircle%28-5%2C-2%2C0.2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Here is the intersection of the 2 regions represented by the series of dots (which is the solution set). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );