document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96755>Question 96755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve by the substitution method x+3y=-8,4x-3y=23 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70385 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=70385\">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( "  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=1%2Ax%2B3%2Ay=-8 ALIGN=MIDDLE  ALT=\"1%2Ax%2B3%2Ay=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax-3%2Ay=23 ALIGN=MIDDLE  ALT=\"4%2Ax-3%2Ay=23\"   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=3%2Ay=-8-1%2Ax ALIGN=MIDDLE  ALT=\"3%2Ay=-8-1%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax ALIGN=MIDDLE  ALT=\"1%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=%28-8-1%2Ax%29%2F3 ALIGN=MIDDLE  ALT=\"y=%28-8-1%2Ax%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3. <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=-8%2F3-%281%2F3%29%2Ax ALIGN=MIDDLE  ALT=\"y=-8%2F3-%281%2F3%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=-8%2F3-%281%2F3%29%2Ax ALIGN=MIDDLE  ALT=\"-8%2F3-%281%2F3%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=-8%2F3-%281%2F3%29%2Ax ALIGN=MIDDLE  ALT=\"-8%2F3-%281%2F3%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=4%2Ax%2B-3%2Ahighlight%28%28-8%2F3-%281%2F3%29%2Ax%29%29=23 ALIGN=MIDDLE  ALT=\"4%2Ax%2B-3%2Ahighlight%28%28-8%2F3-%281%2F3%29%2Ax%29%29=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2F3-%281%2F3%29%2Ax ALIGN=MIDDLE  ALT=\"-8%2F3-%281%2F3%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=4%2Ax-3%2A%28-8%2F3%29-3%28-1%2F3%29x=23 ALIGN=MIDDLE  ALT=\"4%2Ax-3%2A%28-8%2F3%29-3%28-1%2F3%29x=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute -3 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2F3-%281%2F3%29%2Ax ALIGN=MIDDLE  ALT=\"-8%2F3-%281%2F3%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=4%2Ax%2B24%2F3%2B%283%2F3%29%2Ax=23 ALIGN=MIDDLE  ALT=\"4%2Ax%2B24%2F3%2B%283%2F3%29%2Ax=23\"   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=4%2Ax%2B8%2B1%2Ax=23 ALIGN=MIDDLE  ALT=\"4%2Ax%2B8%2B1%2Ax=23\"   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=4%2Ax%2B1%2Ax=23-8 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ax=23-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2B1%2Ax=15 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ax=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 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=5%2Ax=15 ALIGN=MIDDLE  ALT=\"5%2Ax=15\"   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%2F5%29%285%2F1%29%29x=%2815%2F1%29%281%2F5%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F5%29%285%2F1%29%29x=%2815%2F1%29%281%2F5%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%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F1 ALIGN=MIDDLE  ALT=\"5%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=15%2F1 ALIGN=MIDDLE  ALT=\"15%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   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=3 ALIGN=MIDDLE  ALT=\"x=3\"   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=3 ALIGN=MIDDLE  ALT=\"x=3\"   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=4%283%29-3%2Ay=23 ALIGN=MIDDLE  ALT=\"4%283%29-3%2Ay=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   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=12-3%2Ay=23 ALIGN=MIDDLE  ALT=\"12-3%2Ay=23\"   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=-3%2Ay=23-12 ALIGN=MIDDLE  ALT=\"-3%2Ay=23-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   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=-3%2Ay=11 ALIGN=MIDDLE  ALT=\"-3%2Ay=11\"   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%2F-3%29%28-3%29%29%2Ay=%2811%2F1%29%281%2F-3%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F-3%29%28-3%29%29%2Ay=%2811%2F1%29%281%2F-3%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-3 ALIGN=MIDDLE  ALT=\"1%2F-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out -3 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=11%2F-3 ALIGN=MIDDLE  ALT=\"y=11%2F-3\"   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=-11%2F3 ALIGN=MIDDLE  ALT=\"y=-11%2F3\"   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=-11%2F3 ALIGN=MIDDLE  ALT=\"y=-11%2F3\"   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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-11%2F3 ALIGN=MIDDLE  ALT=\"y=-11%2F3\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2F3 ALIGN=MIDDLE  ALT=\"-11%2F3\"   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=1%2Ax%2B3%2Ay=-8 ALIGN=MIDDLE  ALT=\"1%2Ax%2B3%2Ay=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax-3%2Ay=23 ALIGN=MIDDLE  ALT=\"4%2Ax-3%2Ay=23\"   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+-13%2C+13%2C+-13.6666666666667%2C+13.6666666666667%2C%0D%0A++++graph%28+500%2C+600%2C+-13%2C+13%2C+-13.6666666666667%2C+13.6666666666667%2C+%28-8-1%2Ax%29%2F3%2C+%2823-4%2Ax%29%2F-3+%29%2C%0D%0A++++blue%28++circle%28+3%2C+-3.66666666666667%2C+0.173333333333333+%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=1%2Ax%2B3%2Ay=-8 ALIGN=MIDDLE  ALT=\"1%2Ax%2B3%2Ay=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax-3%2Ay=23 ALIGN=MIDDLE  ALT=\"4%2Ax-3%2Ay=23\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2F3 ALIGN=MIDDLE  ALT=\"-11%2F3\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2F3 ALIGN=MIDDLE  ALT=\"-11%2F3\"   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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-11%2F3 ALIGN=MIDDLE  ALT=\"y=-11%2F3\"   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=1%2Ax%2B3%2Ay=-8 ALIGN=MIDDLE  ALT=\"1%2Ax%2B3%2Ay=-8\"   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=1%2A%283%29%2B3%2A%28-11%2F3%29=-8 ALIGN=MIDDLE  ALT=\"1%2A%283%29%2B3%2A%28-11%2F3%29=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-11%2F3 ALIGN=MIDDLE  ALT=\"y=-11%2F3\"   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=3-33%2F3=-8 ALIGN=MIDDLE  ALT=\"3-33%2F3=-8\"   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=-24%2F3=-8 ALIGN=MIDDLE  ALT=\"-24%2F3=-8\"   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=-8=-8 ALIGN=MIDDLE  ALT=\"-8=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. Since this equation is true the solution works.<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  So the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2F3 ALIGN=MIDDLE  ALT=\"-11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%2B3%2Ay=-8 ALIGN=MIDDLE  ALT=\"1%2Ax%2B3%2Ay=-8\"   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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-11%2F3 ALIGN=MIDDLE  ALT=\"y=-11%2F3\"   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=4%2Ax-3%2Ay=23 ALIGN=MIDDLE  ALT=\"4%2Ax-3%2Ay=23\"   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=4%2A%283%29-3%2A%28-11%2F3%29=23 ALIGN=MIDDLE  ALT=\"4%2A%283%29-3%2A%28-11%2F3%29=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-11%2F3 ALIGN=MIDDLE  ALT=\"y=-11%2F3\"   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=12%2B33%2F3=23 ALIGN=MIDDLE  ALT=\"12%2B33%2F3=23\"   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=69%2F3=23 ALIGN=MIDDLE  ALT=\"69%2F3=23\"   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=23=23 ALIGN=MIDDLE  ALT=\"23=23\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2F3 ALIGN=MIDDLE  ALT=\"-11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax-3%2Ay=23 ALIGN=MIDDLE  ALT=\"4%2Ax-3%2Ay=23\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2F3 ALIGN=MIDDLE  ALT=\"-11%2F3\"   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=1%2Ax%2B3%2Ay=-8 ALIGN=MIDDLE  ALT=\"1%2Ax%2B3%2Ay=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax-3%2Ay=23 ALIGN=MIDDLE  ALT=\"4%2Ax-3%2Ay=23\"   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" );