document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118519>Question 118519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x-4y=5<BR>\n" );
document.write( "-4x+2y=6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86664 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=86664\">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=3%2Ax-4%2Ay=5 ALIGN=MIDDLE  ALT=\"3%2Ax-4%2Ay=5\"   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%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2Ay=6\"   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=-4%2Ay=5-3%2Ax ALIGN=MIDDLE  ALT=\"-4%2Ay=5-3%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax ALIGN=MIDDLE  ALT=\"3%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=%285-3%2Ax%29%2F-4 ALIGN=MIDDLE  ALT=\"y=%285-3%2Ax%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -4. <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=-5%2F4%2B%283%2F4%29%2Ax ALIGN=MIDDLE  ALT=\"y=-5%2F4%2B%283%2F4%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=-5%2F4%2B%283%2F4%29%2Ax ALIGN=MIDDLE  ALT=\"-5%2F4%2B%283%2F4%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=-5%2F4%2B%283%2F4%29%2Ax ALIGN=MIDDLE  ALT=\"-5%2F4%2B%283%2F4%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%2B2%2Ahighlight%28%28-5%2F4%2B%283%2F4%29%2Ax%29%29=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2Ahighlight%28%28-5%2F4%2B%283%2F4%29%2Ax%29%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F4%2B%283%2F4%29%2Ax ALIGN=MIDDLE  ALT=\"-5%2F4%2B%283%2F4%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=-4%2Ax%2B2%2A%28-5%2F4%29%2B2%283%2F4%29x=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2A%28-5%2F4%29%2B2%283%2F4%29x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute 2 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F4%2B%283%2F4%29%2Ax ALIGN=MIDDLE  ALT=\"-5%2F4%2B%283%2F4%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=-4%2Ax-10%2F4%2B%286%2F4%29%2Ax=6 ALIGN=MIDDLE  ALT=\"-4%2Ax-10%2F4%2B%286%2F4%29%2Ax=6\"   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-5%2F2%2B%283%2F2%29%2Ax=6 ALIGN=MIDDLE  ALT=\"-4%2Ax-5%2F2%2B%283%2F2%29%2Ax=6\"   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%2B%283%2F2%29%2Ax=6%2B5%2F2 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B%283%2F2%29%2Ax=6%2B5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   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=-4%2Ax%2B%283%2F2%29%2Ax=12%2F2%2B5%2F2 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B%283%2F2%29%2Ax=12%2F2%2B5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make 6 into a fraction with a denominator of 2<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Ax%2B%283%2F2%29%2Ax=17%2F2 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B%283%2F2%29%2Ax=17%2F2\"   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=%28-8%2F2%29%2Ax%2B%283%2F2%29x=17%2F2 ALIGN=MIDDLE  ALT=\"%28-8%2F2%29%2Ax%2B%283%2F2%29x=17%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make -4 into a fraction with a denominator of 2<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2F2%29%2Ax=17%2F2 ALIGN=MIDDLE  ALT=\"%28-5%2F2%29%2Ax=17%2F2\"   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%282%2F-5%29%28-5%2F2%29%29x=%2817%2F2%29%282%2F-5%29 ALIGN=MIDDLE  ALT=\"cross%28%282%2F-5%29%28-5%2F2%29%29x=%2817%2F2%29%282%2F-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F-5 ALIGN=MIDDLE  ALT=\"2%2F-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F2 ALIGN=MIDDLE  ALT=\"-5%2F2\"   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=17%2F2 ALIGN=MIDDLE  ALT=\"17%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F-5 ALIGN=MIDDLE  ALT=\"2%2F-5\"   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=-17%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   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%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   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%28-17%2F5%29%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"-4%28-17%2F5%29%2B2%2Ay=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   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=68%2F5%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"68%2F5%2B2%2Ay=6\"   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=2%2Ay=6-68%2F5 ALIGN=MIDDLE  ALT=\"2%2Ay=6-68%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68%2F5 ALIGN=MIDDLE  ALT=\"68%2F5\"   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=2%2Ay=30%2F5-68%2F5 ALIGN=MIDDLE  ALT=\"2%2Ay=30%2F5-68%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make 6 into a fraction with a denominator of 5<BR>\n" );
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document.write( "  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ay=-38%2F5 ALIGN=MIDDLE  ALT=\"2%2Ay=-38%2F5\"   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%2F2%29%282%29%29%2Ay=%28-38%2F5%29%281%2F2%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F2%29%282%29%29%2Ay=%28-38%2F5%29%281%2F2%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%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out 2 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=-38%2F10 ALIGN=MIDDLE  ALT=\"y=-38%2F10\"   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=-19%2F5 ALIGN=MIDDLE  ALT=\"y=-19%2F5\"   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=-19%2F5 ALIGN=MIDDLE  ALT=\"y=-19%2F5\"   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=-17%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-19%2F5 ALIGN=MIDDLE  ALT=\"y=-19%2F5\"   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%2F5 ALIGN=MIDDLE  ALT=\"-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19%2F5 ALIGN=MIDDLE  ALT=\"-19%2F5\"   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" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax-4%2Ay=5 ALIGN=MIDDLE  ALT=\"3%2Ax-4%2Ay=5\"   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%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2Ay=6\"   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+-13.4%2C+13.4%2C+-13.8%2C+13.8%2C%0D%0A++++graph%28+500%2C+600%2C+-13.4%2C+13.4%2C+-13.8%2C+13.8%2C+%285-3%2Ax%29%2F-4%2C+%286--4%2Ax%29%2F2+%29%2C%0D%0A++++blue%28++circle%28+-3.4%2C+-3.8%2C+0.178666666666667+%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=3%2Ax-4%2Ay=5 ALIGN=MIDDLE  ALT=\"3%2Ax-4%2Ay=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Ax%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2Ay=6\"   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%2F5 ALIGN=MIDDLE  ALT=\"-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19%2F5 ALIGN=MIDDLE  ALT=\"-19%2F5\"   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%2F5 ALIGN=MIDDLE  ALT=\"-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19%2F5 ALIGN=MIDDLE  ALT=\"-19%2F5\"   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%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-19%2F5 ALIGN=MIDDLE  ALT=\"y=-19%2F5\"   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-4%2Ay=5 ALIGN=MIDDLE  ALT=\"3%2Ax-4%2Ay=5\"   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=3%2A%28-17%2F5%29-4%2A%28-19%2F5%29=5 ALIGN=MIDDLE  ALT=\"3%2A%28-17%2F5%29-4%2A%28-19%2F5%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-19%2F5 ALIGN=MIDDLE  ALT=\"y=-19%2F5\"   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=-51%2F5%2B76%2F5=5 ALIGN=MIDDLE  ALT=\"-51%2F5%2B76%2F5=5\"   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=25%2F5=5 ALIGN=MIDDLE  ALT=\"25%2F5=5\"   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=5=5 ALIGN=MIDDLE  ALT=\"5=5\"   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%2F5 ALIGN=MIDDLE  ALT=\"-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19%2F5 ALIGN=MIDDLE  ALT=\"-19%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax-4%2Ay=5 ALIGN=MIDDLE  ALT=\"3%2Ax-4%2Ay=5\"   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%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-19%2F5 ALIGN=MIDDLE  ALT=\"y=-19%2F5\"   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%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2Ay=6\"   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%28-17%2F5%29%2B2%2A%28-19%2F5%29=6 ALIGN=MIDDLE  ALT=\"-4%2A%28-17%2F5%29%2B2%2A%28-19%2F5%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F5 ALIGN=MIDDLE  ALT=\"x=-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-19%2F5 ALIGN=MIDDLE  ALT=\"y=-19%2F5\"   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=68%2F5-38%2F5=6 ALIGN=MIDDLE  ALT=\"68%2F5-38%2F5=6\"   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=30%2F5=6 ALIGN=MIDDLE  ALT=\"30%2F5=6\"   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=6=6 ALIGN=MIDDLE  ALT=\"6=6\"   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%2F5 ALIGN=MIDDLE  ALT=\"-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19%2F5 ALIGN=MIDDLE  ALT=\"-19%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Ax%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2Ay=6\"   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%2F5 ALIGN=MIDDLE  ALT=\"-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19%2F5 ALIGN=MIDDLE  ALT=\"-19%2F5\"   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=3%2Ax-4%2Ay=5 ALIGN=MIDDLE  ALT=\"3%2Ax-4%2Ay=5\"   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%2B2%2Ay=6 ALIGN=MIDDLE  ALT=\"-4%2Ax%2B2%2Ay=6\"   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" );