document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112352>Question 112352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this system by substitution and elimination.\r<BR>\n" );
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document.write( "-16x+45y=134<BR>\n" );
document.write( "40x+18y=-45\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81975 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=81975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\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( "  <BR>\n" );
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=-16%2Ax%2B45%2Ay=134 ALIGN=MIDDLE  ALT=\"-16%2Ax%2B45%2Ay=134\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Ax%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2Ay=-45\"   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=45%2Ay=134%2B16%2Ax ALIGN=MIDDLE  ALT=\"45%2Ay=134%2B16%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Ax ALIGN=MIDDLE  ALT=\"16%2Ax\"   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=y=%28134%2B16%2Ax%29%2F45 ALIGN=MIDDLE  ALT=\"y=%28134%2B16%2Ax%29%2F45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 45. <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=134%2F45%2B%2816%2F45%29%2Ax ALIGN=MIDDLE  ALT=\"y=134%2F45%2B%2816%2F45%29%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=134%2F45%2B%2816%2F45%29%2Ax ALIGN=MIDDLE  ALT=\"134%2F45%2B%2816%2F45%29%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=134%2F45%2B%2816%2F45%29%2Ax ALIGN=MIDDLE  ALT=\"134%2F45%2B%2816%2F45%29%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=40%2Ax%2B18%2Ahighlight%28%28134%2F45%2B%2816%2F45%29%2Ax%29%29=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2Ahighlight%28%28134%2F45%2B%2816%2F45%29%2Ax%29%29=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=134%2F45%2B%2816%2F45%29%2Ax ALIGN=MIDDLE  ALT=\"134%2F45%2B%2816%2F45%29%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=40%2Ax%2B18%2A%28134%2F45%29%2B18%2816%2F45%29x=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2A%28134%2F45%29%2B18%2816%2F45%29x=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute 18 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=134%2F45%2B%2816%2F45%29%2Ax ALIGN=MIDDLE  ALT=\"134%2F45%2B%2816%2F45%29%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=40%2Ax%2B2412%2F45%2B%28288%2F45%29%2Ax=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B2412%2F45%2B%28288%2F45%29%2Ax=-45\"   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=40%2Ax%2B268%2F5%2B%2832%2F5%29%2Ax=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B268%2F5%2B%2832%2F5%29%2Ax=-45\"   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=40%2Ax%2B%2832%2F5%29%2Ax=-45-268%2F5 ALIGN=MIDDLE  ALT=\"40%2Ax%2B%2832%2F5%29%2Ax=-45-268%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=268%2F5 ALIGN=MIDDLE  ALT=\"268%2F5\"   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=40%2Ax%2B%2832%2F5%29%2Ax=-225%2F5-268%2F5 ALIGN=MIDDLE  ALT=\"40%2Ax%2B%2832%2F5%29%2Ax=-225%2F5-268%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make -45 into a fraction with a denominator of 5<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Ax%2B%2832%2F5%29%2Ax=-493%2F5 ALIGN=MIDDLE  ALT=\"40%2Ax%2B%2832%2F5%29%2Ax=-493%2F5\"   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=%28200%2F5%29%2Ax%2B%2832%2F5%29x=-493%2F5 ALIGN=MIDDLE  ALT=\"%28200%2F5%29%2Ax%2B%2832%2F5%29x=-493%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make 40 into a fraction with a denominator of 5<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28232%2F5%29%2Ax=-493%2F5 ALIGN=MIDDLE  ALT=\"%28232%2F5%29%2Ax=-493%2F5\"   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%285%2F232%29%28232%2F5%29%29x=%28-493%2F5%29%285%2F232%29 ALIGN=MIDDLE  ALT=\"cross%28%285%2F232%29%28232%2F5%29%29x=%28-493%2F5%29%285%2F232%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F232 ALIGN=MIDDLE  ALT=\"5%2F232\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=232%2F5 ALIGN=MIDDLE  ALT=\"232%2F5\"   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=-493%2F5 ALIGN=MIDDLE  ALT=\"-493%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F232 ALIGN=MIDDLE  ALT=\"5%2F232\"   DISABLED_style= \"max-width:90%; height:auto;\" > (and simplify) we get <BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%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=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%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=40%28-17%2F8%29%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"40%28-17%2F8%29%2B18%2Ay=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the 2nd equation <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-85%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"-85%2B18%2Ay=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Ay=-45%2B85 ALIGN=MIDDLE  ALT=\"18%2Ay=-45%2B85\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85 ALIGN=MIDDLE  ALT=\"85\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Ay=40 ALIGN=MIDDLE  ALT=\"18%2Ay=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the terms on the right side <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281%2F18%29%2818%29%29%2Ay=%2840%2F1%29%281%2F18%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F18%29%2818%29%29%2Ay=%2840%2F1%29%281%2F18%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%2F18 ALIGN=MIDDLE  ALT=\"1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out 18 on the left side.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=40%2F18 ALIGN=MIDDLE  ALT=\"y=40%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the terms on the right side<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2F9 ALIGN=MIDDLE  ALT=\"y=20%2F9\"   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( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2F9 ALIGN=MIDDLE  ALT=\"y=20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---------------------------------Other answer<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  So our solution is <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2F9 ALIGN=MIDDLE  ALT=\"y=20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  which can also look like <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17%2F8 ALIGN=MIDDLE  ALT=\"-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F9 ALIGN=MIDDLE  ALT=\"20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2Ax%2B45%2Ay=134 ALIGN=MIDDLE  ALT=\"-16%2Ax%2B45%2Ay=134\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Ax%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2Ay=-45\"   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( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+600%2C+-12.125%2C+12.125%2C+-12.2222222222222%2C+12.2222222222222%2C%0D%0A++++graph%28+500%2C+600%2C+-12.125%2C+12.125%2C+-12.2222222222222%2C+12.2222222222222%2C+%28134--16%2Ax%29%2F45%2C+%28-45-40%2Ax%29%2F18+%29%2C%0D%0A++++blue%28++circle%28+-2.125%2C+2.22222222222222%2C+0.161666666666667+%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=-16%2Ax%2B45%2Ay=134 ALIGN=MIDDLE  ALT=\"-16%2Ax%2B45%2Ay=134\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Ax%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2Ay=-45\"   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=-17%2F8 ALIGN=MIDDLE  ALT=\"-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F9 ALIGN=MIDDLE  ALT=\"20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >). This verifies our answer. <BR>\n" );
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document.write( "  -----------------------------------------------------------------------------------------------<BR>\n" );
document.write( "  Check:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17%2F8 ALIGN=MIDDLE  ALT=\"-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F9 ALIGN=MIDDLE  ALT=\"20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) into the system of equations<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2F9 ALIGN=MIDDLE  ALT=\"y=20%2F9\"   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=-16%2Ax%2B45%2Ay=134 ALIGN=MIDDLE  ALT=\"-16%2Ax%2B45%2Ay=134\"   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=-16%2A%28-17%2F8%29%2B45%2A%2820%2F9%29=134 ALIGN=MIDDLE  ALT=\"-16%2A%28-17%2F8%29%2B45%2A%2820%2F9%29=134\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2F9 ALIGN=MIDDLE  ALT=\"y=20%2F9\"   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=272%2F8%2B900%2F9=134 ALIGN=MIDDLE  ALT=\"272%2F8%2B900%2F9=134\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9648%2F72=134 ALIGN=MIDDLE  ALT=\"9648%2F72=134\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=134=134 ALIGN=MIDDLE  ALT=\"134=134\"   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=-17%2F8 ALIGN=MIDDLE  ALT=\"-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F9 ALIGN=MIDDLE  ALT=\"20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2Ax%2B45%2Ay=134 ALIGN=MIDDLE  ALT=\"-16%2Ax%2B45%2Ay=134\"   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=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2F9 ALIGN=MIDDLE  ALT=\"y=20%2F9\"   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=40%2Ax%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2Ay=-45\"   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=40%2A%28-17%2F8%29%2B18%2A%2820%2F9%29=-45 ALIGN=MIDDLE  ALT=\"40%2A%28-17%2F8%29%2B18%2A%2820%2F9%29=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F8 ALIGN=MIDDLE  ALT=\"x=-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2F9 ALIGN=MIDDLE  ALT=\"y=20%2F9\"   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=-680%2F8%2B360%2F9=-45 ALIGN=MIDDLE  ALT=\"-680%2F8%2B360%2F9=-45\"   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=-3240%2F72=-45 ALIGN=MIDDLE  ALT=\"-3240%2F72=-45\"   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=-45=-45 ALIGN=MIDDLE  ALT=\"-45=-45\"   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=-17%2F8 ALIGN=MIDDLE  ALT=\"-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F9 ALIGN=MIDDLE  ALT=\"20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Ax%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2Ay=-45\"   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=-17%2F8 ALIGN=MIDDLE  ALT=\"-17%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F9 ALIGN=MIDDLE  ALT=\"20%2F9\"   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=-16%2Ax%2B45%2Ay=134 ALIGN=MIDDLE  ALT=\"-16%2Ax%2B45%2Ay=134\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Ax%2B18%2Ay=-45 ALIGN=MIDDLE  ALT=\"40%2Ax%2B18%2Ay=-45\"   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( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );