document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110604>Question 110604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> using the two equations below, solve for x and y using three different methods, substituion, addition and graphing.\r<BR>\n" );
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document.write( "-2x+3y=6<BR>\n" );
document.write( "3x-5y=-11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80825 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=80825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using the two equations below, solve for x and y using three different methods, substitution, addition and graphing.<BR>\n" );
document.write( "-2x + 3y = 6<BR>\n" );
document.write( " 3x - 5y =-11<BR>\n" );
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document.write( "Substitution:<BR>\n" );
document.write( "Rearrange the 1st equation to be used for subsitution:<BR>\n" );
document.write( "3y = 2x + 6<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F3 ALIGN=MIDDLE  ALT=\"6%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >; divided equation by 3<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2<BR>\n" );
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document.write( "Substitute (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2) for y in the 2nd equation:<BR>\n" );
document.write( "3x - 5(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2) = -11<BR>\n" );
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document.write( "3x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F3 ALIGN=MIDDLE  ALT=\"10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - 10 = -11<BR>\n" );
document.write( ";<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F3 ALIGN=MIDDLE  ALT=\"9%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F3 ALIGN=MIDDLE  ALT=\"10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = -11 + 10<BR>\n" );
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document.write( "-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = -1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = 1; multiplied by -1 to get rid of the negatives<BR>\n" );
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document.write( "x = 3; Multiplied by 3 to get rid of the fraction<BR>\n" );
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document.write( "Find y using the y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >3 + 2<BR>\n" );
document.write( "y = 2 + 2<BR>\n" );
document.write( "y = 4<BR>\n" );
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document.write( "Our solution x = 3; y = 4<BR>\n" );
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document.write( "Substitute for x and y in the 2nd equation to confirm our solutions:<BR>\n" );
document.write( "3x - 5y =-11<BR>\n" );
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document.write( "3(3) - 5(4) =<BR>\n" );
document.write( "9 - 20 = -11<BR>\n" );
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document.write( "Elimination:<BR>\n" );
document.write( "-2x + 3y = 6<BR>\n" );
document.write( " 3x - 5y =-11<BR>\n" );
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document.write( "Multiply the 1st equation by 3 and the 2nd equation by 2:<BR>\n" );
document.write( "-6x + 9y = 18<BR>\n" );
document.write( "+6x -10y = -22<BR>\n" );
document.write( "---------------adding eliminates x, find y:<BR>\n" );
document.write( "0x - 1y = -4<BR>\n" );
document.write( "y = +4<BR>\n" );
document.write( "Find x just like we did before using substitution for y in either equation<BR>\n" );
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document.write( "To graph this:<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2; from above:<BR>\n" );
document.write( "and<BR>\n" );
document.write( " 3x - 5y =-11<BR>\n" );
document.write( "-5y = - 3x - 11<BR>\n" );
document.write( "5y = 3x + 11; multiplied by -1 to get rid of all those negatives<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F5 ALIGN=MIDDLE  ALT=\"11%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Plot these to equations, should look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-6%2C+8%2C+-2%2C+5%2C+%282%2F3%29x+%2B2%2C+.6x%2B%2811%2F5%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-6%2C+8%2C+-2%2C+5%2C+%282%2F3%29x+%2B2%2C+.6x%2B%2811%2F5%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Not very clear but they should intersect at x=3, y=4<BR>\n" );
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document.write( "How about this? Did it explain these three methods to you?<BR>\n" );
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