document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998985>Question 998985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need some help with this problem:<BR>\n" );
document.write( "4/3x+3/2y=-4/3<BR>\n" );
document.write( "-16/9x-2y=16/9<BR>\n" );
document.write( "I'm using the addition/elimination method.\r<BR>\n" );
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document.write( "I just don't know what to multiply to the top equation<BR>\n" );
document.write( "to make one of the variables cancel out. please help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616658 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=616658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume your system is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29 ALIGN=MIDDLE  ALT=\"system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are fractions in those equations, and they make mistakes more probable, so I would get rid of them first.<BR>\n" );
document.write( "To get rid of fractions in an equation, we can multiply both sides of the equal sign times a multiple of all the denominators to get an equivalent equation.<BR>\n" );
document.write( "Shown baby step, by baby step, it looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29x%2B%283%2F2%29y=-4%2F3 ALIGN=MIDDLE  ALT=\"%284%2F3%29x%2B%283%2F2%29y=-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%28%284%2F3%29x%2B%283%2F2%29y%29=6%2A%28-4%2F3%29 ALIGN=MIDDLE  ALT=\"6%2A%28%284%2F3%29x%2B%283%2F2%29y%29=6%2A%28-4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%284%2F3%29x%2B6%2A%283%2F2%29y=-8%29 ALIGN=MIDDLE  ALT=\"6%2A%284%2F3%29x%2B6%2A%283%2F2%29y=-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B9y=-8%29 ALIGN=MIDDLE  ALT=\"8x%2B9y=-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Working with the other equation in a similar way we get to a much nicer system.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29 ALIGN=MIDDLE  ALT=\"system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288x%2B9y=-8%2C-16x-18y=16%29 ALIGN=MIDDLE  ALT=\"system%288x%2B9y=-8%2C-16x-18y=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x-18y=16 ALIGN=MIDDLE  ALT=\"-16x-18y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be simplified by<BR>\n" );
document.write( "dividing both sides of the equal sign by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x-18y=16 ALIGN=MIDDLE  ALT=\"-16x-18y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%2F2-18y%2F2=16%2F2 ALIGN=MIDDLE  ALT=\"-16x%2F2-18y%2F2=16%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x-9y=8 ALIGN=MIDDLE  ALT=\"-8x-9y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With that we get an equivalent system that is really user-friendly:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29 ALIGN=MIDDLE  ALT=\"system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288x%2B9y=-8%2C-16x-18y=16%29 ALIGN=MIDDLE  ALT=\"system%288x%2B9y=-8%2C-16x-18y=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288x%2B9y=-8%2C-8x-9y=8%29 ALIGN=MIDDLE  ALT=\"system%288x%2B9y=-8%2C-8x-9y=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Now you realized that the second equation is the first equation multiplied times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "They are equivalent equation that would graph as the same line.<BR>\n" );
document.write( "There are infinite solutions: all the points on that line.<BR>\n" );
document.write( "The system is dependent.\r<BR>\n" );
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