document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120383>Question 120383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 53/24 and the difference of the same two numbers is 13/24.  What are the numbers?\r<BR>\n" );
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document.write( "I got lost with the fractions... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88238 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=88238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the \"sum of two numbers is 53/24\" then we have the first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=53%2F24 ALIGN=MIDDLE  ALT=\"x%2By=53%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If the \"difference of the same two numbers is 13/24\" then we have the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=13%2F24 ALIGN=MIDDLE  ALT=\"x-y=13%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solving_linear_system_by_substitution.solver>Solving a linear system of equations by subsitution</A></TD></TR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2Ax%2B%281%29%2Ay=53%2F24 ALIGN=MIDDLE  ALT=\"%281%29%2Ax%2B%281%29%2Ay=53%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%28%281%29%2Ax%2B%281%29%2Ay%29=%2824%29%2A%2853%2F24%29 ALIGN=MIDDLE  ALT=\"24%28%281%29%2Ax%2B%281%29%2Ay%29=%2824%29%2A%2853%2F24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 24<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ay=53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ay=53\"   DISABLED_style= \"max-width:90%; height:auto;\" >Distribute and simplify<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2Ax%2B%28-1%29%2Ay=13%2F24 ALIGN=MIDDLE  ALT=\"%281%29%2Ax%2B%28-1%29%2Ay=13%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%28%281%29%2Ax%2B%28-1%29%2Ay%29=%2824%29%2A%2813%2F24%29 ALIGN=MIDDLE  ALT=\"24%28%281%29%2Ax%2B%28-1%29%2Ay%29=%2824%29%2A%2813%2F24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 24<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2Ax%2B-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and simplify<BR>\n" );
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document.write( "  Lets start with the given system of linear equations<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ay=53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ay=53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2Ax-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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 choose y.<BR>\n" );
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document.write( "  Solve for y for the first equation <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ay=53-24%2Ax ALIGN=MIDDLE  ALT=\"24%2Ay=53-24%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax ALIGN=MIDDLE  ALT=\"24%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2853-24%2Ax%29%2F24 ALIGN=MIDDLE  ALT=\"y=%2853-24%2Ax%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 24. <BR>\n" );
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document.write( "  Which breaks down and reduces to <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=53%2F24-1%2Ax ALIGN=MIDDLE  ALT=\"y=53%2F24-1%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we've fully isolated y<BR>\n" );
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document.write( "  Since y equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53%2F24-1%2Ax ALIGN=MIDDLE  ALT=\"53%2F24-1%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can substitute the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53%2F24-1%2Ax ALIGN=MIDDLE  ALT=\"53%2F24-1%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > into y of the 2nd equation. This will eliminate y so we can solve for x.<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B-24%2Ahighlight%28%2853%2F24-1%2Ax%29%29=13 ALIGN=MIDDLE  ALT=\"24%2Ax%2B-24%2Ahighlight%28%2853%2F24-1%2Ax%29%29=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53%2F24-1%2Ax ALIGN=MIDDLE  ALT=\"53%2F24-1%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since this eliminates y, we can now solve for x.<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-24%2A%2853%2F24%29-24%28-1%29x=13 ALIGN=MIDDLE  ALT=\"24%2Ax-24%2A%2853%2F24%29-24%28-1%29x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute -24 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53%2F24-1%2Ax ALIGN=MIDDLE  ALT=\"53%2F24-1%2Ax\"   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=24%2Ax-1272%2F24%2B24%2Ax=13 ALIGN=MIDDLE  ALT=\"24%2Ax-1272%2F24%2B24%2Ax=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-53%2B24%2Ax=13 ALIGN=MIDDLE  ALT=\"24%2Ax-53%2B24%2Ax=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ax=13%2B53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ax=13%2B53\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53 ALIGN=MIDDLE  ALT=\"53\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ax=66 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ax=66\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the terms on the right side<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Ax=66 ALIGN=MIDDLE  ALT=\"48%2Ax=66\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine the terms on the left side.  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281%2F48%29%2848%2F1%29%29x=%2866%2F1%29%281%2F48%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F48%29%2848%2F1%29%29x=%2866%2F1%29%281%2F48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F48 ALIGN=MIDDLE  ALT=\"1%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2F1 ALIGN=MIDDLE  ALT=\"48%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and isolate x<BR>\n" );
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document.write( "  So when we multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66%2F1 ALIGN=MIDDLE  ALT=\"66%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F48 ALIGN=MIDDLE  ALT=\"1%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > (and simplify) we get <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---------------------------------One answer<BR>\n" );
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document.write( "   Now that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, lets substitute that in for x to solve for y<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2811%2F8%29-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2811%2F8%29-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the 2nd equation <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33-24%2Ay=13 ALIGN=MIDDLE  ALT=\"33-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24%2Ay=13-33 ALIGN=MIDDLE  ALT=\"-24%2Ay=13-33\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33 ALIGN=MIDDLE  ALT=\"33\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24%2Ay=-20 ALIGN=MIDDLE  ALT=\"-24%2Ay=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the terms on the right side <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281%2F-24%29%28-24%29%29%2Ay=%28-20%2F1%29%281%2F-24%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F-24%29%28-24%29%29%2Ay=%28-20%2F1%29%281%2F-24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F-24 ALIGN=MIDDLE  ALT=\"1%2F-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out -24 on the left side.<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-20%2F-24 ALIGN=MIDDLE  ALT=\"y=-20%2F-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the terms on the right side<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F6 ALIGN=MIDDLE  ALT=\"y=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  So this is the other answer<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F6 ALIGN=MIDDLE  ALT=\"y=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---------------------------------Other answer<BR>\n" );
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document.write( "  So our solution is <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F6 ALIGN=MIDDLE  ALT=\"y=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  which can also look like <BR>\n" );
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document.write( "  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  Notice if we graph the equations (if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ay=53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ay=53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2Ax-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  we get <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+600%2C+-11.375%2C+11.375%2C+-10.8333333333333%2C+10.8333333333333%2C%0D%0A++++graph%28+500%2C+600%2C+-11.375%2C+11.375%2C+-10.8333333333333%2C+10.8333333333333%2C+%2853-24%2Ax%29%2F24%2C+%2813-24%2Ax%29%2F-24+%29%2C%0D%0A++++blue%28++circle%28+1.375%2C+0.833333333333333%2C+0.151666666666667+%29+%29+%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ay=53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ay=53\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2Ax-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.<BR>\n" );
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document.write( "  and we can see that the two equations intersect at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >). This verifies our answer. <BR>\n" );
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document.write( "  Check:<BR>\n" );
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document.write( "  Plug in (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) into the system of equations<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F6 ALIGN=MIDDLE  ALT=\"y=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now plug those values into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ay=53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ay=53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2A%2811%2F8%29%2B24%2A%285%2F6%29=53 ALIGN=MIDDLE  ALT=\"24%2A%2811%2F8%29%2B24%2A%285%2F6%29=53\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F6 ALIGN=MIDDLE  ALT=\"y=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=264%2F8%2B120%2F6=53 ALIGN=MIDDLE  ALT=\"264%2F8%2B120%2F6=53\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1272%2F24=53 ALIGN=MIDDLE  ALT=\"1272%2F24=53\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53=53 ALIGN=MIDDLE  ALT=\"53=53\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. Since this equation is true the solution works.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ay=53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ay=53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F6 ALIGN=MIDDLE  ALT=\"y=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now plug those values into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2Ax-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2A%2811%2F8%29-24%2A%285%2F6%29=13 ALIGN=MIDDLE  ALT=\"24%2A%2811%2F8%29-24%2A%285%2F6%29=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F8 ALIGN=MIDDLE  ALT=\"x=11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F6 ALIGN=MIDDLE  ALT=\"y=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=264%2F8-120%2F6=13 ALIGN=MIDDLE  ALT=\"264%2F8-120%2F6=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=312%2F24=13 ALIGN=MIDDLE  ALT=\"312%2F24=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13=13 ALIGN=MIDDLE  ALT=\"13=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. Since this equation is true the solution works.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2Ax-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies the system of equations<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%2B24%2Ay=53 ALIGN=MIDDLE  ALT=\"24%2Ax%2B24%2Ay=53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax-24%2Ay=13 ALIGN=MIDDLE  ALT=\"24%2Ax-24%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  this verifies our answer.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The two numbers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );