document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124486>Question 124486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1000x+30y=500<BR>\n" );
document.write( "x-2y=11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91233 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=91233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Do you want to solve by 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%281000x%2B30y=500%2Cx-2y=11%29 ALIGN=MIDDLE  ALT=\"system%281000x%2B30y=500%2Cx-2y=11%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=1000x%2B30y=500 ALIGN=MIDDLE  ALT=\"1000x%2B30y=500\"   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=30y=500-1000x ALIGN=MIDDLE  ALT=\"30y=500-1000x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000x ALIGN=MIDDLE  ALT=\"1000x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30y=-1000x%2B500 ALIGN=MIDDLE  ALT=\"30y=-1000x%2B500\"   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=%28-1000x%2B500%29%2F%2830%29 ALIGN=MIDDLE  ALT=\"y=%28-1000x%2B500%29%2F%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   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%28-1000%29%2F%2830%29%29x%2B%28500%29%2F%2830%29 ALIGN=MIDDLE  ALT=\"y=%28%28-1000%29%2F%2830%29%29x%2B%28500%29%2F%2830%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=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"y=%28-100%2F3%29x%2B50%2F3\"   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=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"y=%28-100%2F3%29x%2B50%2F3\"   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=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"%28-100%2F3%29x%2B50%2F3\"   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-2highlight%28%28%28-100%2F3%29x%2B50%2F3%29%29=11 ALIGN=MIDDLE  ALT=\"x-2highlight%28%28%28-100%2F3%29x%2B50%2F3%29%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"y=%28-100%2F3%29x%2B50%2F3\"   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=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"%28-100%2F3%29x%2B50%2F3\"   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%28-2%29%28-100%2F3%29x%2B%28-2%29%2850%2F3%29=11 ALIGN=MIDDLE  ALT=\"x%2B%28-2%29%28-100%2F3%29x%2B%28-2%29%2850%2F3%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"%28-100%2F3%29x%2B50%2F3\"   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%2B%28200%2F3%29x-100%2F3=11 ALIGN=MIDDLE  ALT=\"x%2B%28200%2F3%29x-100%2F3=11\"   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=%283%29%281x%2B%28200%2F3%29x-100%2F3%29=%283%29%2811%29 ALIGN=MIDDLE  ALT=\"%283%29%281x%2B%28200%2F3%29x-100%2F3%29=%283%29%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCM of 3. 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=3x%2B200x-100=33 ALIGN=MIDDLE  ALT=\"3x%2B200x-100=33\"   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=203x-100=33 ALIGN=MIDDLE  ALT=\"203x-100=33\"   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=203x=33%2B100 ALIGN=MIDDLE  ALT=\"203x=33%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 100 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=203x=133 ALIGN=MIDDLE  ALT=\"203x=133\"   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=%28133%29%2F%28203%29 ALIGN=MIDDLE  ALT=\"x=%28133%29%2F%28203%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 203 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=19%2F29 ALIGN=MIDDLE  ALT=\"x=19%2F29\"   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=19%2F29 ALIGN=MIDDLE  ALT=\"x=19%2F29\"   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=19%2F29 ALIGN=MIDDLE  ALT=\"x=19%2F29\"   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=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"y=%28-100%2F3%29x%2B50%2F3\"   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=%28-100%2F3%29x%2B50%2F3 ALIGN=MIDDLE  ALT=\"y=%28-100%2F3%29x%2B50%2F3\"   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=%28-100%2F3%29%2819%2F29%29%2B50%2F3 ALIGN=MIDDLE  ALT=\"y=%28-100%2F3%29%2819%2F29%29%2B50%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=19%2F29 ALIGN=MIDDLE  ALT=\"x=19%2F29\"   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=-1900%2F87%2B50%2F3 ALIGN=MIDDLE  ALT=\"y=-1900%2F87%2B50%2F3\"   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=-150%2F29 ALIGN=MIDDLE  ALT=\"y=-150%2F29\"   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=-150%2F29 ALIGN=MIDDLE  ALT=\"y=-150%2F29\"   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=19%2F29 ALIGN=MIDDLE  ALT=\"x=19%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-150%2F29 ALIGN=MIDDLE  ALT=\"y=-150%2F29\"   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{19}{29},-\frac{150}{29}\right)\"> \r<BR>\n" );
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