document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113307>Question 113307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by graphing.<BR>\n" );
document.write( "	x – 2y = 8<BR>\n" );
document.write( "	x + y = –1<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 #82466 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To graph an equation of a straight line, you only need to determine two points.  Pick a value for x and then solve for y to give a point on the line.  Do this twice for each line.   Once you have your two points determined, plot them and connect the dots with a straight line.\r<BR>\n" );
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document.write( "I'll do the first one:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=8 ALIGN=MIDDLE  ALT=\"x-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  I pick the value 4 for x first.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-2y=8 ALIGN=MIDDLE  ALT=\"4-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=4 ALIGN=MIDDLE  ALT=\"-2y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >   So now we know that one point is (4, -2).  We'll call that point A\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=8 ALIGN=MIDDLE  ALT=\"x-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  I pick the value 0 for x next.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-2y=8 ALIGN=MIDDLE  ALT=\"0-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >   So our other point is (0, -4).  We'll call that point B\r<BR>\n" );
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document.write( "I'll leave you to figure two points for the second equation, but I'll show a graph of both lines so that we can see where the simultaneous solution point occurs.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28400%2C400%2C+-7%2C7%2C-7%2C7%2C%0D%0A+++++++++++grid%281%29%2C%0D%0Alocate%28.2%2C+-4.2%2C+A%28+0%2C+-4+%29+%29%2C%0D%0Alocate%284.2%2C+-2.2%2C+B%28+4%2C+-2+%29+%29%2C%0D%0A+++++++++++green%28line%28-10%2C-9%2C10%2C1%29%29%2C%0D%0A+++++++++++blue%28line%2810%2C-11%2C-10%2C9%29%29%2C%0D%0A+++++++++++red%28circle%280%2C-4%2C0.2%29%29%2C%0D%0A+++++++++++red%28circle%284%2C-2%2C.2%29%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It looks like the lines intersect at (2, -3).\r<BR>\n" );
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document.write( "Let's check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-2%28-3%29=2%2B6=8 ALIGN=MIDDLE  ALT=\"2-2%28-3%29=2%2B6=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the point is on one of the lines.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B%28-3%29=-1 ALIGN=MIDDLE  ALT=\"2%2B%28-3%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the point is on the other line as well and the answer checks. </SPAN>\n" );
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