document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164302>Question 164302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the linear system and estimate the solution. Then check the solution algebraically.\r<BR>\n" );
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document.write( "x+2y=9<BR>\n" );
document.write( "-x+6y=-1\r<BR>\n" );
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document.write( "thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121116 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=121116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Transform both to slope-intercept form and graph.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=9 ALIGN=MIDDLE  ALT=\"x%2B2y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=9-x ALIGN=MIDDLE  ALT=\"2y=9-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%289-x%29%2F2 ALIGN=MIDDLE  ALT=\"y=%289-x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Slope = -1/2, Y-intercept=9/2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B6y=-1 ALIGN=MIDDLE  ALT=\"-x%2B6y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=x-1 ALIGN=MIDDLE  ALT=\"6y=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-1%29%2F6 ALIGN=MIDDLE  ALT=\"y=%28x-1%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Slope=1/6, Y-intercept=-1/6 <BR>\n" );
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document.write( "Then graph the two lines. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-2%2C+10%2C+-5%2C+5%2Cgrid%28+1+%29%2Ccircle%28+7%2C+1%2C+.2+%29%2C+graph%28+300%2C+300%2C+-2%2C+10%2C+-5%2C+5%2C+%289-x%29%2F2%2C+%28x-1%29%2F6%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Looks like (7,1) is the solution.<BR>\n" );
document.write( "Check using the equations. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=9 ALIGN=MIDDLE  ALT=\"x%2B2y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2B2%281%29=9 ALIGN=MIDDLE  ALT=\"7%2B2%281%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2B2=9 ALIGN=MIDDLE  ALT=\"7%2B2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=9 ALIGN=MIDDLE  ALT=\"9=9\"   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=-x%2B6y=-1 ALIGN=MIDDLE  ALT=\"-x%2B6y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2B6%281%29=-1 ALIGN=MIDDLE  ALT=\"-7%2B6%281%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2B6=-1 ALIGN=MIDDLE  ALT=\"-7%2B6=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=-1 ALIGN=MIDDLE  ALT=\"-1=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution was verified using both equations. <BR>\n" );
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document.write( "Now the algebraic solution.  <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=9 ALIGN=MIDDLE  ALT=\"x%2B2y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B6y=-1 ALIGN=MIDDLE  ALT=\"-x%2B6y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add eq. 1 and eq. 2 to get rid of x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y%2B%28-x%29%2B6y=9-1 ALIGN=MIDDLE  ALT=\"x%2B2y%2B%28-x%29%2B6y=9-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y=8 ALIGN=MIDDLE  ALT=\"8y=8\"   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%29 ALIGN=MIDDLE  ALT=\"highlight%28y=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then from eq. 1,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=9 ALIGN=MIDDLE  ALT=\"x%2B2y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%281%29=9 ALIGN=MIDDLE  ALT=\"x%2B2%281%29=9\"   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=7%29 ALIGN=MIDDLE  ALT=\"highlight%28x=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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