document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=125259>Question 125259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help solve by substitution<BR>\n" );
document.write( "9x+5y=28<BR>\n" );
document.write( "3x+9y=-42\r<BR>\n" );
document.write( "\n" );
document.write( "Please show all your steps, I doing something wrong and can't seem to figure out what it is.  thank you in advance for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91807 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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( "  <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=9%2Ax%2B5%2Ay=28 ALIGN=MIDDLE  ALT=\"9%2Ax%2B5%2Ay=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2Ay=-42\"   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=5%2Ay=28-9%2Ax ALIGN=MIDDLE  ALT=\"5%2Ay=28-9%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Ax ALIGN=MIDDLE  ALT=\"9%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=%2828-9%2Ax%29%2F5 ALIGN=MIDDLE  ALT=\"y=%2828-9%2Ax%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5. <BR>\n" );
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document.write( "  Which breaks down and reduces to <BR>\n" );
document.write( "  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=28%2F5-%289%2F5%29%2Ax ALIGN=MIDDLE  ALT=\"y=28%2F5-%289%2F5%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=28%2F5-%289%2F5%29%2Ax ALIGN=MIDDLE  ALT=\"28%2F5-%289%2F5%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=28%2F5-%289%2F5%29%2Ax ALIGN=MIDDLE  ALT=\"28%2F5-%289%2F5%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=3%2Ax%2B9%2Ahighlight%28%2828%2F5-%289%2F5%29%2Ax%29%29=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2Ahighlight%28%2828%2F5-%289%2F5%29%2Ax%29%29=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%2F5-%289%2F5%29%2Ax ALIGN=MIDDLE  ALT=\"28%2F5-%289%2F5%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since this eliminates y, we can now solve for x.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2B9%2A%2828%2F5%29%2B9%28-9%2F5%29x=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2A%2828%2F5%29%2B9%28-9%2F5%29x=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute 9 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%2F5-%289%2F5%29%2Ax ALIGN=MIDDLE  ALT=\"28%2F5-%289%2F5%29%2Ax\"   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=3%2Ax%2B252%2F5-%2881%2F5%29%2Ax=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B252%2F5-%2881%2F5%29%2Ax=-42\"   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=3%2Ax%2B252%2F5-%2881%2F5%29%2Ax=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B252%2F5-%2881%2F5%29%2Ax=-42\"   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=3%2Ax-%2881%2F5%29%2Ax=-42-252%2F5 ALIGN=MIDDLE  ALT=\"3%2Ax-%2881%2F5%29%2Ax=-42-252%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=252%2F5 ALIGN=MIDDLE  ALT=\"252%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=3%2Ax-%2881%2F5%29%2Ax=-210%2F5-252%2F5 ALIGN=MIDDLE  ALT=\"3%2Ax-%2881%2F5%29%2Ax=-210%2F5-252%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make -42 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=3%2Ax-%2881%2F5%29%2Ax=-462%2F5 ALIGN=MIDDLE  ALT=\"3%2Ax-%2881%2F5%29%2Ax=-462%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=%2815%2F5%29%2Ax-%2881%2F5%29x=-462%2F5 ALIGN=MIDDLE  ALT=\"%2815%2F5%29%2Ax-%2881%2F5%29x=-462%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make 3 into a fraction with a denominator of 5<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-66%2F5%29%2Ax=-462%2F5 ALIGN=MIDDLE  ALT=\"%28-66%2F5%29%2Ax=-462%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%2F-66%29%28-66%2F5%29%29x=%28-462%2F5%29%285%2F-66%29 ALIGN=MIDDLE  ALT=\"cross%28%285%2F-66%29%28-66%2F5%29%29x=%28-462%2F5%29%285%2F-66%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%2F-66 ALIGN=MIDDLE  ALT=\"5%2F-66\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-66%2F5 ALIGN=MIDDLE  ALT=\"-66%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=-462%2F5 ALIGN=MIDDLE  ALT=\"-462%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F-66 ALIGN=MIDDLE  ALT=\"5%2F-66\"   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=7 ALIGN=MIDDLE  ALT=\"x=7\"   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=7 ALIGN=MIDDLE  ALT=\"x=7\"   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=3%287%29%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"3%287%29%2B9%2Ay=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   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=21%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"21%2B9%2Ay=-42\"   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=9%2Ay=-42-21 ALIGN=MIDDLE  ALT=\"9%2Ay=-42-21\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Ay=-63 ALIGN=MIDDLE  ALT=\"9%2Ay=-63\"   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%2F9%29%289%29%29%2Ay=%28-63%2F1%29%281%2F9%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F9%29%289%29%29%2Ay=%28-63%2F1%29%281%2F9%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%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out 9 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=-63%2F9 ALIGN=MIDDLE  ALT=\"y=-63%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the terms on the right side<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   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=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   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=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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=9%2Ax%2B5%2Ay=28 ALIGN=MIDDLE  ALT=\"9%2Ax%2B5%2Ay=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2Ay=-42\"   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+-17%2C+17%2C+-17%2C+17%2C%0D%0A++++graph%28+500%2C+600%2C+-17%2C+17%2C+-17%2C+17%2C+%2828-9%2Ax%29%2F5%2C+%28-42-3%2Ax%29%2F9+%29%2C%0D%0A++++blue%28++circle%28+7%2C+-7%2C+0.226666666666667+%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=9%2Ax%2B5%2Ay=28 ALIGN=MIDDLE  ALT=\"9%2Ax%2B5%2Ay=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2Ay=-42\"   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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   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=9%2Ax%2B5%2Ay=28 ALIGN=MIDDLE  ALT=\"9%2Ax%2B5%2Ay=28\"   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=9%2A%287%29%2B5%2A%28-7%29=28 ALIGN=MIDDLE  ALT=\"9%2A%287%29%2B5%2A%28-7%29=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=63-35=28 ALIGN=MIDDLE  ALT=\"63-35=28\"   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=28=28 ALIGN=MIDDLE  ALT=\"28=28\"   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=28=28 ALIGN=MIDDLE  ALT=\"28=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. Since this equation is true the solution works.<BR>\n" );
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document.write( "  So the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Ax%2B5%2Ay=28 ALIGN=MIDDLE  ALT=\"9%2Ax%2B5%2Ay=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   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=3%2Ax%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2Ay=-42\"   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=3%2A%287%29%2B9%2A%28-7%29=-42 ALIGN=MIDDLE  ALT=\"3%2A%287%29%2B9%2A%28-7%29=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   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=21-63=-42 ALIGN=MIDDLE  ALT=\"21-63=-42\"   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=-42=-42 ALIGN=MIDDLE  ALT=\"-42=-42\"   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=-42=-42 ALIGN=MIDDLE  ALT=\"-42=-42\"   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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2Ay=-42\"   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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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=9%2Ax%2B5%2Ay=28 ALIGN=MIDDLE  ALT=\"9%2Ax%2B5%2Ay=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2B9%2Ay=-42 ALIGN=MIDDLE  ALT=\"3%2Ax%2B9%2Ay=-42\"   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><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );