document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=868806>Question 868806</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by graphing. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.)\r<BR>\n" );
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document.write( "y = 2x &#8722; 7<BR>\n" );
document.write( "x &#8722; 2y = &#8722;4<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 #523842 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=523842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=2x-7%2Cx-2y=-4%29 ALIGN=MIDDLE  ALT=\"system%28y=2x-7%2Cx-2y=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a system of linear equations.<BR>\n" );
document.write( "The graph of a linear equation is a straight line,<BR>\n" );
document.write( "so to graph a linear equation all we need to do is plot two points,<BR>\n" );
document.write( "and draw the line that goes through those two points.<BR>\n" );
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document.write( "Step 1: We graph each equation as a straight line.<BR>\n" );
document.write( "Step 2: We look up the coordinates of the intersection point from the graph.<BR>\n" );
document.write( "Step 3: We verify that those coordinates are a solution.<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28y=2x-7%29 ALIGN=MIDDLE  ALT=\"blue%28y=2x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<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=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point (0,-7).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2A5-7 ALIGN=MIDDLE  ALT=\"y=2%2A5-7\"   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;\" > gives us point (5,3).<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x-2y=-4%29 ALIGN=MIDDLE  ALT=\"red%28x-2y=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<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=-2y=-4 ALIGN=MIDDLE  ALT=\"-2y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <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;\" > gives us point (0,2).<BR>\n" );
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;\" > --> <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 (-4,0).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-5%2C10%2C-9%2C6%2C%0D%0Agrid%281%29%2Cblue%28circle%280%2C-7%2C0.2%29%29%2C%0D%0Ablue%28circle%285%2C3%2C0.2%29%29%2Cblue%28line%28-1%2C-9%2C7%2C7%29%29%2C%0D%0Ared%28circle%280%2C2%2C0.2%29%29%2Cred%28circle%28-4%2C0%2C0.2%29%29%2C%0D%0Ared%28line%28-6%2C-1%2C10%2C7%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The lines seen to intersect at (6,5), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=6%2Cy=5%29 ALIGN=MIDDLE  ALT=\"system%28x=6%2Cy=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so we need to verify that those values satisfy the equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=6%2Cy=5%29 ALIGN=MIDDLE  ALT=\"system%28x=6%2Cy=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x-7=2%2A6-7=12-7=5=y%2Cx-2y=6-2%2A5=6-10=-4%29 ALIGN=MIDDLE  ALT=\"system%282x-7=2%2A6-7=12-7=5=y%2Cx-2y=6-2%2A5=6-10=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So (6,5) or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=6%2Cy=5%29 ALIGN=MIDDLE  ALT=\"system%28x=6%2Cy=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the solution.<BR>\n" );
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document.write( "NOTE:<BR>\n" );
document.write( "If the two lines had been parallel, there would be no solution.<BR>\n" );
document.write( "If the two equation graphed as the same line, there would be infinitely many solutions. </SPAN>\n" );
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