document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=342318>Question 342318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve for x and y, and then graph these equations?\r<BR>\n" );
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document.write( "8x + 2y = 7<BR>\n" );
document.write( "3x - 4y = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244993 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=244993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Multiply the first equation by 2 and add them,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%2B4y%2B3x-4y=14%2B5 ALIGN=MIDDLE  ALT=\"16x%2B4y%2B3x-4y=14%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19x=19 ALIGN=MIDDLE  ALT=\"19x=19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then use either equation to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%29-4y=5 ALIGN=MIDDLE  ALT=\"3%281%29-4y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y=2 ALIGN=MIDDLE  ALT=\"-4y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-1%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Convert both equations to slope intercept form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+%2B+2y+=+7 ALIGN=MIDDLE  ALT=\"8x+%2B+2y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-8x%2B7 ALIGN=MIDDLE  ALT=\"2y=-8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4x%2B7%2F2 ALIGN=MIDDLE  ALT=\"y=-4x%2B7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot the y-intercept (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "Then use the slope to calculate another point on the line. <BR>\n" );
document.write( "Slope is change in y over change in x. <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > changes by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > will change by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-4%29=-8 ALIGN=MIDDLE  ALT=\"2%28-4%29=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "Another point on the line would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0%2B2=2 ALIGN=MIDDLE  ALT=\"x=0%2B2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%2F2%2B2%28-4%29=-9%2F2 ALIGN=MIDDLE  ALT=\"y=7%2F2%2B2%28-4%29=-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2F2 ALIGN=MIDDLE  ALT=\"-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+-5%2C5%2C-5%2C5%2Ccircle%280%2C7%2F2%2C0.2%29%2Ccircle%282%2C-9%2F2%2C0.2%29%2Cgrid%281%29%2Cgraph%28300%2C300%2C+-5%2C5%2C-5%2C5%2C-4x%2B7%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-+4y+=+5 ALIGN=MIDDLE  ALT=\"3x+-+4y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y=-3x%2B5 ALIGN=MIDDLE  ALT=\"-4y=-3x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F4%29x-5%2F4 ALIGN=MIDDLE  ALT=\"y=%283%2F4%29x-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Plot the y-intercept (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F4 ALIGN=MIDDLE  ALT=\"-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "Then use the slope to calculate another point on the line. <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > changes by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > will change by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%283%2F4%29=3 ALIGN=MIDDLE  ALT=\"4%283%2F4%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "Another point on the line would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0%2B4=4 ALIGN=MIDDLE  ALT=\"x=0%2B4=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=-5%2F4%2B3=7%2F4 ALIGN=MIDDLE  ALT=\"y=-5%2F4%2B3=7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F4 ALIGN=MIDDLE  ALT=\"7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+-5%2C5%2C-5%2C5%2Ccircle%280%2C-5%2F4%2C0.2%29%2Ccircle%284%2C7%2F4%2C0.2%29%2Ccircle%281%2C-1%2F2%2C0.2%29%2Ccircle%280%2C7%2F2%2C0.2%29%2Ccircle%282%2C-9%2F2%2C0.2%29%2Cgrid%281%29%2Cgraph%28300%2C300%2C-5%2C5%2C-5%2C5%2C-4x%2B7%2F2%2C%283%2F4%29x-5%2F4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note the intersection of the lines occurs at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) as previously determined algebraically. </SPAN>\n" );
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