document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201962>Question 201962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help Needed;\r<BR>\n" );
document.write( "\n" );
document.write( "Graph the feasible region for the system of inequalities.\r<BR>\n" );
document.write( "\n" );
document.write( "3x - 2y &#8804; 6<BR>\n" );
document.write( "x - y &#8805; 0<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152255 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=152255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given system of inequalities\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y%3C=6 ALIGN=MIDDLE  ALT=\"3x-2y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%3E=0 ALIGN=MIDDLE  ALT=\"x-y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In order to graph this system of inequalities, we need to graph each inequality one at a time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First lets graph the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y%3C=6 ALIGN=MIDDLE  ALT=\"3x-2y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y%3C=6 ALIGN=MIDDLE  ALT=\"3x-2y%3C=6\"   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=3x-2y=6 ALIGN=MIDDLE  ALT=\"3x-2y=6\"   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=3x-2y=6 ALIGN=MIDDLE  ALT=\"3x-2y=6\"   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" );
document.write( "\n" );
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+%283%2F2%29x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%283%2F2%29x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=6 ALIGN=MIDDLE  ALT=\"3x-2y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
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=3x-2y%3C=6 ALIGN=MIDDLE  ALT=\"3x-2y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the test point\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute (0,0) into the inequality\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%280%29-2%280%29%3C=6 ALIGN=MIDDLE  ALT=\"3%280%29-2%280%29%3C=6\"   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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=6 ALIGN=MIDDLE  ALT=\"0%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of <a  rel=nofollow HREF=http://www.mozilla.com/en-US/firefox/>Firefox</a> to see these images.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since this inequality is true, we simply shade the entire region that contains (0,0)\r<BR>\n" );
document.write( "\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%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B3%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B9%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B15%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B21%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B27%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B30%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B33%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B39%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B42%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B45%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B48%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=3x-2y%3C=6 ALIGN=MIDDLE  ALT=\"3x-2y%3C=6\"   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=3x-2y=6 ALIGN=MIDDLE  ALT=\"3x-2y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > in red) and the shaded region (in green) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets graph the second inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%3E=0 ALIGN=MIDDLE  ALT=\"x-y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%3E=0 ALIGN=MIDDLE  ALT=\"x-y%3E=0\"   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=x-y=0 ALIGN=MIDDLE  ALT=\"x-y=0\"   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=x-y=0 ALIGN=MIDDLE  ALT=\"x-y=0\"   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" );
document.write( "\n" );
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+x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=0 ALIGN=MIDDLE  ALT=\"x-y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Now lets pick a test point, say (0,1). 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=x-y%3E=0 ALIGN=MIDDLE  ALT=\"x-y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the test point\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute (0,1) into the inequality\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29-%281%29%3E=0 ALIGN=MIDDLE  ALT=\"%280%29-%281%29%3E=0\"   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=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3E=0 ALIGN=MIDDLE  ALT=\"1%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since this inequality is true, we simply shade the entire region that contains (0,1)\r<BR>\n" );
document.write( "\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%2Cx%2Cx%2B-3%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-9%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-15%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-21%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-27%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-30%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-33%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-39%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-42%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-45%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%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=x-y%3E=0 ALIGN=MIDDLE  ALT=\"x-y%3E=0\"   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=x-y=0 ALIGN=MIDDLE  ALT=\"x-y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > in red) and the shaded region (in green) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we essentially have these 2 regions:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Region #1<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%2C%283%2F2%29x-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B48%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=3x-2y%3C=6 ALIGN=MIDDLE  ALT=\"3x-2y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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%2Cx%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%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=x-y%3E=0 ALIGN=MIDDLE  ALT=\"x-y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "<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+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%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%283%2F2%29x-3%2C%283%2F2%29x-3%2B48%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2Cx%2Cx%2B-48%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<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( "<BR>\n" );
document.write( "<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+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%2C%283%2F2%29x-3%2Cx%29%2Ccircle%28-20%2C-20%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%28-14%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%28-11%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%28-8%2C-14%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%28-5%2C-8%2C0.2%29%2C%0D%0Acircle%28-5%2C-5%2C0.2%29%2C%0D%0Acircle%28-2%2C-5%2C0.2%29%2C%0D%0Acircle%28-2%2C-2%2C0.2%29%2C%0D%0Acircle%281%2C1%2C0.2%29%2C%0D%0Acircle%284%2C4%2C0.2%29%2C%0D%0Acircle%28-20%2C-20%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%28-14%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%28-11%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%28-8%2C-14%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%28-5%2C-8%2C0.2%29%2C%0D%0Acircle%28-5%2C-5%2C0.2%29%2C%0D%0Acircle%28-2%2C-5%2C0.2%29%2C%0D%0Acircle%28-2%2C-2%2C0.2%29%2C%0D%0Acircle%281%2C1%2C0.2%29%2C%0D%0Acircle%284%2C4%2C0.2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Here is the intersection of the 2 regions represented by the series of dots </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );