document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077257>Question 1077257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to solve the linear equations by graphing? <BR>\n" );
document.write( "y=4x+2 y=x+17<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 #691777 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=691777\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve the linear equations by graphing, you<BR>\n" );
document.write( "1) plot both equations on the same graph<BR>\n" );
document.write( "2) find the coordinates of the intersection point<BR>\n" );
document.write( "3) verify that the pair (x,y) of coordinates found is a solution of both equations<BR>\n" );
document.write( " <BR>\n" );
document.write( "1) The graph for a linear equation is a straight line.<BR>\n" );
document.write( "To draw it you just need to know two points.<BR>\n" );
document.write( "The graph for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B17%29 ALIGN=MIDDLE  ALT=\"y=x%2B17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > obviously passes through point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+0+%2C+17+%29%22 ALIGN=MIDDLE  ALT=\"%22%28+0+%2C+17+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting a value for x in the equation, you can get another point.<BR>\n" );
document.write( "Picking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8%2B17=25 ALIGN=MIDDLE  ALT=\"y=8%2B17=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+8+%2C+25+%29%22 ALIGN=MIDDLE  ALT=\"%22%28+8+%2C+25+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > is another point in the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B17%29 ALIGN=MIDDLE  ALT=\"y=x%2B17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "To get the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B17%29 ALIGN=MIDDLE  ALT=\"y=x%2B17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you plot those two points and connect them with a straight line.<BR>\n" );
document.write( "Similarly, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%2B2%29 ALIGN=MIDDLE  ALT=\"y=4x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you could use point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+0+%2C+2+%29%22 ALIGN=MIDDLE  ALT=\"%22%28+0+%2C+2+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+7+%2C+30+%29%22 ALIGN=MIDDLE  ALT=\"%22%28+7+%2C+30+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The graph for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28red%28y=4x%2B2%29%2Cgreen%28y=x%2B17%29%29 ALIGN=MIDDLE  ALT=\"system%28red%28y=4x%2B2%29%2Cgreen%28y=x%2B17%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "could look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-4%2C36%2Cgrid%281%29%2C%0D%0Ared%28line%28-2%2C-6%2C9%2C38%29%29%2C%0D%0Agreen%28line%28-2%2C15%2C9%2C26%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) The lines seem to cross at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+5+%2C+22+%29%22 ALIGN=MIDDLE  ALT=\"%22%28+5+%2C+22+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=5%2Cy=22%29 ALIGN=MIDDLE  ALT=\"system%28x=5%2Cy=22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "3) substituting <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;\" > into the two equations, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2A5%2B2=20%2B2=22 ALIGN=MIDDLE  ALT=\"y=4%2A5%2B2=20%2B2=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2B17=22 ALIGN=MIDDLE  ALT=\"y=5%2B17=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which verifies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=5%2Cy=22%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=5%2Cy=22%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "as the solution to the system of linear equations. </SPAN>\n" );
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