document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018252>Question 1018252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I graph the solution set of the system of inequalities or indicate that the system has no solution<BR>\n" );
document.write( "8x+6y>6<BR>\n" );
document.write( "2x+y<8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634463 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=634463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graphing one linear equation, or one inequality can be tough.<BR>\n" );
document.write( "You start by deciding on the scale to be used for the x-axis and the y-axis.<BR>\n" );
document.write( "You may start with -10 to 10 on both axes, and see how it looks.<BR>\n" );
document.write( "If it does not look good, you may have to re-do the graph.<BR>\n" );
document.write( "When you have two inequalities, it can be torture,<BR>\n" );
document.write( "because the scale that makes each graph look good for one inequality<BR>\n" );
document.write( "may not look good for the two of them together.<BR>\n" );
document.write( "Thinking and planning ahead may save time and pain,<BR>\n" );
document.write( "and may allow to skip up to the solution of the system of inequalities,<BR>\n" );
document.write( "without having to graph each inequality separately first.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The graph for any linear inequality has one solid or dashed boundary line,<BR>\n" );
document.write( "and the region of the x-y plane to one side of that line, colored or shaded.<BR>\n" );
document.write( "(The boundary line is dashed when the inequality sign is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%3C%22 ALIGN=MIDDLE  ALT=\"%22%3C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%3E%22 ALIGN=MIDDLE  ALT=\"%22%3E%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and it is solid if the sign includes an \"or equal\").<BR>\n" );
document.write( " <BR>\n" );
document.write( "A system of linear inequalities can have boundary lines that intersect. In that case, the graph of the solution is one of the four angles formed by those boundary lines (colored or shaded), with the boundary rays dashed or solid, depending on the inequality sign. <BR>\n" );
document.write( " <BR>\n" );
document.write( "The graph of the solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288x%2B6y%3E6%2C2x%2By%3C8%29 ALIGN=MIDDLE  ALT=\"system%288x%2B6y%3E6%2C2x%2By%3C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will consist of two dashed rays (portions of the dashed boundary lines for each inequality),<BR>\n" );
document.write( "with a colored or shaded angle between them.<BR>\n" );
document.write( "Unfortunately for you, the two lines intersect at a point quite far from the origin,<BR>\n" );
document.write( "and since your graph needs to show the x- and y-axes, it needs to show the origin.<BR>\n" );
document.write( "Showing the origin and the intersection between the two lines makes for an ugly graph,<BR>\n" );
document.write( "with a weird scale, but that is what was asked for.<BR>\n" );
document.write( "Feel free to use a different scale.<BR>\n" );
document.write( "The lines intersect at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288x%2B6y=6%2C2x%2By=8%29 ALIGN=MIDDLE  ALT=\"system%288x%2B6y=6%2C2x%2By=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=10.5%2Cy=-13%29 ALIGN=MIDDLE  ALT=\"system%28x=10.5%2Cy=-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I will leave the original lines showing as faint green traces<BR>\n" );
document.write( "(they are not part of the solution, and could be erased).<BR>\n" );
document.write( "To draw those lines, you can use the intersection point, along with points (0,1) and (4,0).<BR>\n" );
document.write( "I will draw the solution as black dashed boundary lines,<BR>\n" );
document.write( "and I will fill with red-line shading the angle region that is the solution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C18%2C-18%2C2%2Cgrid%280%29%2C%0D%0Aline%283.5%2C1%2C3%2C2%29%2Cline%284.5%2C-1%2C4%2C0%29%2C%0D%0Aline%286%2C-4%2C5.5%2C-3%29%2Cline%287.5%2C-7%2C7%2C-6%29%2C%0D%0Aline%288.5%2C-9%2C9%2C-10%29%2Cline%2810%2C-12%2C10.5%2C-13%29%2C%0D%0Agreen%28arrow%2810.5%2C-13%2C13.5%2C-19%29%29%2Cgreen%28arrow%2810.5%2C-13%2C15%2C-19%29%29%2C%0D%0Aline%2810.5%2C-13%2C9.9%2C-12.2%29%2Cline%288.1%2C-9.8%2C7.5%2C-9%29%2C%0D%0Aline%285.7%2C-6.6%2C5.1%2C-5.8%29%2Cline%283.3%2C-3.4%2C2.7%2C-2.6%29%2Cline%283.3%2C-3.4%2C2.7%2C-2.6%29%2C%0D%0Aline%280.9%2C-0.2%2C0.3%2C0.6%29%2Cred%28line%28-0.3%2C1.4%2C3.3%2C1.4%29%29%2C%0D%0Ared%28line%280.3%2C0.6%2C3.7%2C0.6%29%29%2Cred%28line%280.9%2C-0.2%2C4.1%2C-0.2%29%29%2C%0D%0Ared%28line%281.5%2C-1%2C4.5%2C-1%29%29%2Cred%28line%282.1%2C-1.8%2C4.9%2C-1.8%29%29%2C%0D%0Ared%28line%282.7%2C-2.6%2C5.3%2C-2.6%29%29%2Cred%28line%283.3%2C-3.4%2C5.7%2C-3.4%29%29%2C%0D%0Ared%28line%283.9%2C-4.2%2C6.1%2C-4.2%29%29%2Cred%28line%284.5%2C-5%2C6.5%2C-5%29%29%2C%0D%0Ared%28line%285.1%2C-5.8%2C6.9%2C-5.8%29%29%2Cred%28line%285.7%2C-6.6%2C7.3%2C-6.6%29%29%2C%0D%0Ared%28line%286.3%2C-7.4%2C7.7%2C-7.4%29%29%2Cred%28line%286.9%2C-8.2%2C8.1%2C-8.2%29%29%2C%0D%0Ared%28line%286.3%2C-7.4%2C7.7%2C-7.4%29%29%2Cred%28line%286.9%2C-8.2%2C8.1%2C-8.2%29%29%2C%0D%0Ared%28line%287.5%2C-9%2C8.5%2C-9%29%29%2Cred%28line%288.1%2C-9.8%2C8.9%2C-9.8%29%29%2C%0D%0Ared%28line%288.7%2C-10.6%2C9.3%2C-10.6%29%29%2Cred%28line%289.3%2C-11.4%2C9.7%2C-11.4%29%29%2C%0D%0Ared%28line%289.9%2C-12.2%2C10.1%2C-12.2%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The point (2,0) in the angle shaded can be used as a check point to verify the solution.<BR>\n" );
document.write( " <BR>\n" );
document.write( "FOR REFERENCE, THIS IS HOW THE INDIVIDUAL INEQUALITIES WOULD BE GRAPHED:<BR>\n" );
document.write( "The inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%3C8 ALIGN=MIDDLE  ALT=\"2x%2By%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents all the point in the x-y coordinate plane to one side of the line given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=8 ALIGN=MIDDLE  ALT=\"2x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , not including the boundary line.<BR>\n" );
document.write( "To graph that inequality, you would graph the boundary line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=8 ALIGN=MIDDLE  ALT=\"2x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a dashed line,<BR>\n" );
document.write( "and you would color or shade the side that represents <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%3C8 ALIGN=MIDDLE  ALT=\"2x%2By%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "To graph a line, you need two points.<BR>\n" );
document.write( "In the case of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=8 ALIGN=MIDDLE  ALT=\"2x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the points that seem easiest to find are those with <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;\" > or <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;\" > .<BR>\n" );
document.write( "For <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;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A0%2By=8 ALIGN=MIDDLE  ALT=\"2%2A0%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2By=8 ALIGN=MIDDLE  ALT=\"0%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%280%2C8%29 ALIGN=MIDDLE  ALT=\"A%280%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For <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;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B0=8 ALIGN=MIDDLE  ALT=\"2x%2B0=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=8 ALIGN=MIDDLE  ALT=\"2x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2F2 ALIGN=MIDDLE  ALT=\"x=8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%284%2C0%29 ALIGN=MIDDLE  ALT=\"B%284%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "To graph the line you locate points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > an d draw the line that connects them.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-1%2C9%2C%0D%0Agrid%281%29%2Cline%285%2C-2%2C-1%2C10%29%2C%0D%0Acircle%280%2C8%2C0.15%29%2Ccircle%284%2C0%2C0.15%29%2C%0D%0Alocate%280.1%2C8.5%2CA%29%2Clocate%284.1%2C0.5%2CB%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%3C8 ALIGN=MIDDLE  ALT=\"2x%2By%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is graphed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-1%2C9%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28300%2C300%2C-1%2C9%2C-1%2C9%2C2x%2By%3C7.9%29%2C%0D%0Aline%284.5%2C-1%2C4%2C0%29%2Cline%283%2C2%2C2.5%2C3%29%2C%0D%0Aline%281.5%2C5%2C1%2C6%29%2Cline%280%2C8%2C-0.5%2C9%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , with the line dashed,<BR>\n" );
document.write( "and the side containing the origin colored,<BR>\n" );
document.write( "because (0,0) , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=0%2Cy=0%29 ALIGN=MIDDLE  ALT=\"system%28x=0%2Cy=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one point of the solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%3C8 ALIGN=MIDDLE  ALT=\"2x%2By%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A0%2B0=0%2B0=0%3C8 ALIGN=MIDDLE  ALT=\"2%2A0%2B0=0%2B0=0%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y%3E6 ALIGN=MIDDLE  ALT=\"8x%2B6y%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents all the point in the x-y coordinate plane to one side of the line given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y=6 ALIGN=MIDDLE  ALT=\"8x%2B6y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , not including the boundary line.<BR>\n" );
document.write( "To graph that inequality, you would graph the boundary line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y=6 ALIGN=MIDDLE  ALT=\"8x%2B6y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a dashed line,<BR>\n" );
document.write( "and you would color or shade the side that represents <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y%3E6 ALIGN=MIDDLE  ALT=\"8x%2B6y%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In the case of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y=6 ALIGN=MIDDLE  ALT=\"8x%2B6y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the points with <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;\" > or <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;\" > are easy to find, but are too close to each other to help you draw the line.<BR>\n" );
document.write( "You can use <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;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A0%2B6y=6 ALIGN=MIDDLE  ALT=\"8%2A0%2B6y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B6y=6 ALIGN=MIDDLE  ALT=\"0%2B6y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=6 ALIGN=MIDDLE  ALT=\"6y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6%2F6 ALIGN=MIDDLE  ALT=\"y=6%2F6\"   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;\" > ,<BR>\n" );
document.write( "which gives us point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%280%2C1%29 ALIGN=MIDDLE  ALT=\"C%280%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but <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;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6%2A0=6 ALIGN=MIDDLE  ALT=\"8x%2B6%2A0=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B0=6 ALIGN=MIDDLE  ALT=\"8x%2B0=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=6 ALIGN=MIDDLE  ALT=\"8x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2F8 ALIGN=MIDDLE  ALT=\"x=6%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F4=0.75 ALIGN=MIDDLE  ALT=\"x=3%2F4=0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%283%2F4%2C0%29 ALIGN=MIDDLE  ALT=\"D%283%2F4%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which is so close to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > that you cannot draw a good line.<BR>\n" );
document.write( "Instead, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A6%2B6y=6 ALIGN=MIDDLE  ALT=\"8%2A6%2B6y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2By%296=6 ALIGN=MIDDLE  ALT=\"%288%2By%296=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2By=6%2F6 ALIGN=MIDDLE  ALT=\"8%2By=6%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2By=1 ALIGN=MIDDLE  ALT=\"8%2By=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1-8 ALIGN=MIDDLE  ALT=\"y=1-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%286%2C-7%29 ALIGN=MIDDLE  ALT=\"E%286%2C-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So you would graph the line as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-8%2C2%2C%0D%0Agrid%281%29%2Ccircle%280%2C1%2C0.15%29%2C%0D%0Acircle%286%2C-7%2C0.15%29%2Cline%28-3%2C5%2C9%2C-11%29%2C%0D%0Alocate%280.1%2C1.5%2CC%29%2Clocate%286.1%2C-6.5%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , and the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y%3E6 ALIGN=MIDDLE  ALT=\"8x%2B6y%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >} as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-8%2C2%2C%0D%0Agrid%281%29%2Cgraph%28300%2C300%2C-1%2C9%2C-8%2C2%2C4x%2B3y%3E3.2%29%2C%0D%0Aline%28-1.2%2C2.6%2C-0.6%2C1.8%29%2Cline%280.6%2C0.2%2C1.2%2C-0.6%29%2C%0D%0Aline%282.4%2C-2.2%2C3%2C-3%29%2Cline%284.2%2C-4.6%2C4.8%2C-5.4%29%2C%0D%0Aline%286%2C-7%2C6.6%2C-7.8%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with the colored part not including the origin,<BR>\n" );
document.write( "because (0,0) , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=0%2Cy=0%29 ALIGN=MIDDLE  ALT=\"system%28x=0%2Cy=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not part of the solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y%3E6 ALIGN=MIDDLE  ALT=\"8x%2B6y%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A0%2B6%2A0=0%2B0=0%3C6 ALIGN=MIDDLE  ALT=\"8%2A0%2B6%2A0=0%2B0=0%3C6\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );