document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128750>Question 128750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I know these questions are easy for you guys but I just don't retain any algebra at all. I try my best before I consult you. On that note can you help me refresh my memory on this graphing type problem? I need to solve by graphing.<BR>\n" );
document.write( "Do I need points for this question? If I do  I will use x = points 0 ,-1, 1 and<BR>\n" );
document.write( "Do I need points for Y ? Can you show me the easiest way? I really appreciate all your help, I really do! This problem is a handout and is not in a book. Thanks so much.\r<BR>\n" );
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document.write( "         x-2y=0  and  2x-y= -3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94186 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=94186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's graph the first equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=0 ALIGN=MIDDLE  ALT=\"x-2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Let's find a point using <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=0 ALIGN=MIDDLE  ALT=\"x-2y=0\"   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=0-2y=0 ALIGN=MIDDLE  ALT=\"0-2y=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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=0 ALIGN=MIDDLE  ALT=\"-2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%2F-2 ALIGN=MIDDLE  ALT=\"y=0%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2 to isolate y\r<BR>\n" );
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document.write( "<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;\" > Reduce\r<BR>\n" );
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document.write( "So when <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=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So our first point is (0,0)\r<BR>\n" );
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document.write( "Let's find another point using <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=0 ALIGN=MIDDLE  ALT=\"x-2y=0\"   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=1-2y=0 ALIGN=MIDDLE  ALT=\"1-2y=0\"   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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=-1 ALIGN=MIDDLE  ALT=\"-2y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2F-2 ALIGN=MIDDLE  ALT=\"y=-1%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2 to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F2 ALIGN=MIDDLE  ALT=\"y=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So when <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%2F2 ALIGN=MIDDLE  ALT=\"y=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So our second point is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,\frac{1}{2}\right)\">\r<BR>\n" );
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document.write( "Now plot the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,0\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,\frac{1}{2}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C0%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C0%2C0.1%29%2C%0D%0Acircle%280%2C0%2C0.12%29%2C%0D%0Acircle%280%2C0%2C0.15%29%2C%0D%0Acircle%281%2C1%2F2%2C0.1%29%2C%0D%0Acircle%281%2C1%2F2%2C0.12%29%2C%0D%0Acircle%281%2C1%2F2%2C0.15%29%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now draw a straight line through the two points. This line is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=0 ALIGN=MIDDLE  ALT=\"x-2y=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=drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C%281%2F2%29x%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C0%2C0.1%29%2C%0D%0Acircle%280%2C0%2C0.12%29%2C%0D%0Acircle%280%2C0%2C0.15%29%2C%0D%0Acircle%281%2C1%2F2%2C0.1%29%2C%0D%0Acircle%281%2C1%2F2%2C0.12%29%2C%0D%0Acircle%281%2C1%2F2%2C0.15%29%0D%0A%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-2y=0 ALIGN=MIDDLE  ALT=\"x-2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the two points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,0\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,\frac{1}{2}\right)\">\r<BR>\n" );
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document.write( "Let's graph the second equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=+-3 ALIGN=MIDDLE  ALT=\"2x-y=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Let's find a point using <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=+-3 ALIGN=MIDDLE  ALT=\"2x-y=+-3\"   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=2%280%29-y=+-3 ALIGN=MIDDLE  ALT=\"2%280%29-y=+-3\"   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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y=-3 ALIGN=MIDDLE  ALT=\"-y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2F-1 ALIGN=MIDDLE  ALT=\"y=-3%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So when <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=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So our first point is (0,3)\r<BR>\n" );
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document.write( "Let's find another point using <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=+-3 ALIGN=MIDDLE  ALT=\"2x-y=+-3\"   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=2%281%29-y=+-3 ALIGN=MIDDLE  ALT=\"2%281%29-y=+-3\"   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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-y=+-3 ALIGN=MIDDLE  ALT=\"2-y=+-3\"   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=-y=-5 ALIGN=MIDDLE  ALT=\"-y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%2F-1 ALIGN=MIDDLE  ALT=\"y=-5%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So when <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=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So our second point is (1,5)\r<BR>\n" );
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document.write( "Now plot the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,3\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,5\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C0%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C3%2C0.1%29%2C%0D%0Acircle%280%2C3%2C0.12%29%2C%0D%0Acircle%280%2C3%2C0.15%29%2C%0D%0Acircle%281%2C5%2C0.1%29%2C%0D%0Acircle%281%2C5%2C0.12%29%2C%0D%0Acircle%281%2C5%2C0.15%29%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now draw a straight line through the two points. This line is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=+-3 ALIGN=MIDDLE  ALT=\"2x-y=+-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=drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C%28-3-2x%29%2F%28-1%29%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C3%2C0.1%29%2C%0D%0Acircle%280%2C3%2C0.12%29%2C%0D%0Acircle%280%2C3%2C0.15%29%2C%0D%0Acircle%281%2C5%2C0.1%29%2C%0D%0Acircle%281%2C5%2C0.12%29%2C%0D%0Acircle%281%2C5%2C0.15%29%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=+-3 ALIGN=MIDDLE  ALT=\"2x-y=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the two points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,3\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,5\right)\">\r<BR>\n" );
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document.write( "Now simply graph these two line together to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C%28-3-2x%29%2F%28-1%29%2C%281%2F2%29x%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C3%2C0.1%29%2C%0D%0Acircle%280%2C3%2C0.12%29%2C%0D%0Acircle%280%2C3%2C0.15%29%2C%0D%0Acircle%281%2C5%2C0.1%29%2C%0D%0Acircle%281%2C5%2C0.12%29%2C%0D%0Acircle%281%2C5%2C0.15%29%2C%0D%0Acircle%280%2C0%2C0.1%29%2C%0D%0Acircle%280%2C0%2C0.12%29%2C%0D%0Acircle%280%2C0%2C0.15%29%2C%0D%0Acircle%281%2C1%2F2%2C0.1%29%2C%0D%0Acircle%281%2C1%2F2%2C0.12%29%2C%0D%0Acircle%281%2C1%2F2%2C0.15%29%2C%0D%0Ablue%28circle%28-2%2C-1%2C0.1%29%29%2C%0D%0Ablue%28circle%28-2%2C-1%2C0.12%29%29%2C%0D%0Ablue%28circle%28-2%2C-1%2C0.15%29%29%0D%0A%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-2y=0 ALIGN=MIDDLE  ALT=\"x-2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=+-3 ALIGN=MIDDLE  ALT=\"2x-y=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red)\r<BR>\n" );
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document.write( "From the graph, we can see that the two lines intersect at the point (-2,-1) (blue point) </SPAN>\n" );
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