document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127880>Question 127880</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -4x-6y=7<BR>\n" );
document.write( "x+5y=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93663 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you want to solve using substitution?\r<BR>\n" );
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document.write( "Start with the given system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-4x-6y=7%2Cx%2B5y=8%29 ALIGN=MIDDLE  ALT=\"system%28-4x-6y=7%2Cx%2B5y=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
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document.write( "So let's isolate y in the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-6y=7 ALIGN=MIDDLE  ALT=\"-4x-6y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6y=7%2B4x ALIGN=MIDDLE  ALT=\"-6y=7%2B4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6y=%2B4x%2B7 ALIGN=MIDDLE  ALT=\"-6y=%2B4x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%2B4x%2B7%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"y=%28%2B4x%2B7%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28%2B4%29%2F%28-6%29%29x%2B%287%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"y=%28%28%2B4%29%2F%28-6%29%29x%2B%287%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5highlight%28%28%28-2%2F3%29x-7%2F6%29%29=8 ALIGN=MIDDLE  ALT=\"x%2B5highlight%28%28%28-2%2F3%29x-7%2F6%29%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B%285%29%28-2%2F3%29x%2B%285%29%28-7%2F6%29=8 ALIGN=MIDDLE  ALT=\"x%2B%285%29%28-2%2F3%29x%2B%285%29%28-7%2F6%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%2810%2F3%29x-35%2F6=8 ALIGN=MIDDLE  ALT=\"x-%2810%2F3%29x-35%2F6=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%29%281x-%2810%2F3%29x-35%2F6%29=%286%29%288%29 ALIGN=MIDDLE  ALT=\"%286%29%281x-%2810%2F3%29x-35%2F6%29=%286%29%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCM of 6. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-20x-35=48 ALIGN=MIDDLE  ALT=\"6x-20x-35=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply the LCM to each side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x-35=48 ALIGN=MIDDLE  ALT=\"-14x-35=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x=48%2B35 ALIGN=MIDDLE  ALT=\"-14x=48%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 35 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x=83 ALIGN=MIDDLE  ALT=\"-14x=83\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2883%29%2F%28-14%29 ALIGN=MIDDLE  ALT=\"x=%2883%29%2F%28-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -14 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-83%2F14 ALIGN=MIDDLE  ALT=\"x=-83%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "-----------------First Answer------------------------------\r<BR>\n" );
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document.write( "So the first part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-83%2F14 ALIGN=MIDDLE  ALT=\"x=-83%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-83%2F14 ALIGN=MIDDLE  ALT=\"x=-83%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can plug it into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we previously solved 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;\" > in the first equation).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29x-7%2F6 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29x-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the equation where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > was previously isolated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29%28-83%2F14%29-7%2F6 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%28-83%2F14%29-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-83%2F14 ALIGN=MIDDLE  ALT=\"x=-83%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=166%2F42-7%2F6 ALIGN=MIDDLE  ALT=\"y=166%2F42-7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=39%2F14 ALIGN=MIDDLE  ALT=\"y=39%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms and reduce.  (note: if you need help with fractions, check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver\">solver</a>)\r<BR>\n" );
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document.write( "-----------------Second Answer------------------------------\r<BR>\n" );
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document.write( "So the second part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=39%2F14 ALIGN=MIDDLE  ALT=\"y=39%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------Summary------------------------------\r<BR>\n" );
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document.write( "So our answers are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-83%2F14 ALIGN=MIDDLE  ALT=\"x=-83%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=39%2F14 ALIGN=MIDDLE  ALT=\"y=39%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which form the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\frac{83}{14},\frac{39}{14}\right)\"> \r<BR>\n" );
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