document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945604>Question 945604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need to solve this by using elimination method.\r<BR>\n" );
document.write( "\n" );
document.write( "2x+9y=3.75<BR>\n" );
document.write( "x+y=6.5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576781 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=576781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B9y=3.75 ALIGN=MIDDLE  ALT=\"2x%2B9y=3.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B9y=15%2F4 ALIGN=MIDDLE  ALT=\"2x%2B9y=15%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > I will use this one, it will work better with this solver<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=6.5 ALIGN=MIDDLE  ALT=\"x%2By=6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=13%2F2 ALIGN=MIDDLE  ALT=\"x%2By=13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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_elimination.solver>Solving a System of Linear Equations by Elimination/Addition</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2Ax%2B%289%29%2Ay=15%2F4 ALIGN=MIDDLE  ALT=\"%282%29%2Ax%2B%289%29%2Ay=15%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28%282%29%2Ax%2B%289%29%2Ay%29=%284%29%2A%2815%2F4%29 ALIGN=MIDDLE  ALT=\"4%28%282%29%2Ax%2B%289%29%2Ay%29=%284%29%2A%2815%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 4<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax%2B36%2Ay=15 ALIGN=MIDDLE  ALT=\"8%2Ax%2B36%2Ay=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >Distribute and simplify<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  ------------------------------------------<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2Ax%2B%281%29%2Ay=13%2F2 ALIGN=MIDDLE  ALT=\"%281%29%2Ax%2B%281%29%2Ay=13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%281%29%2Ax%2B%281%29%2Ay%29=%282%29%2A%2813%2F2%29 ALIGN=MIDDLE  ALT=\"2%28%281%29%2Ax%2B%281%29%2Ay%29=%282%29%2A%2813%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2B2%2Ay=13 ALIGN=MIDDLE  ALT=\"2%2Ax%2B2%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and simplify<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  -----------------------------------------<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Lets start with the given system of linear equations<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax%2B36%2Ay=15 ALIGN=MIDDLE  ALT=\"8%2Ax%2B36%2Ay=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2B2%2Ay=13 ALIGN=MIDDLE  ALT=\"2%2Ax%2B2%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 8 and 2 to some equal number, we could try to get them to the LCM.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since the LCM of 8 and 2 is 8, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -4 like this:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A%288%2Ax%2B36%2Ay%29=%2815%29%2A1 ALIGN=MIDDLE  ALT=\"1%2A%288%2Ax%2B36%2Ay%29=%2815%29%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the top equation (both sides) by 1<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A%282%2Ax%2B2%2Ay%29=%2813%29%2A-4 ALIGN=MIDDLE  ALT=\"-4%2A%282%2Ax%2B2%2Ay%29=%2813%29%2A-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the bottom equation (both sides) by -4<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So after multiplying we get this:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax%2B36%2Ay=15 ALIGN=MIDDLE  ALT=\"8%2Ax%2B36%2Ay=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2Ax-8%2Ay=-52 ALIGN=MIDDLE  ALT=\"-8%2Ax-8%2Ay=-52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Notice how 8 and -8 add to zero (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B-8=0 ALIGN=MIDDLE  ALT=\"8%2B-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now add the equations together. In order to add 2 equations, group like terms and combine them<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2Ax-8%2Ax%29%2B%2836%2Ay-8%2Ay%29=15-52 ALIGN=MIDDLE  ALT=\"%288%2Ax-8%2Ax%29%2B%2836%2Ay-8%2Ay%29=15-52\"   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=%288-8%29%2Ax%2B%2836-8%29y=15-52 ALIGN=MIDDLE  ALT=\"%288-8%29%2Ax%2B%2836-8%29y=15-52\"   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=cross%288%2B-8%29%2Ax%2B%2836-8%29%2Ay=15-52 ALIGN=MIDDLE  ALT=\"cross%288%2B-8%29%2Ax%2B%2836-8%29%2Ay=15-52\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So after adding and canceling out the x terms we're left with:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%2Ay=-37 ALIGN=MIDDLE  ALT=\"28%2Ay=-37\"   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=y=-37%2F28 ALIGN=MIDDLE  ALT=\"y=-37%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for y<BR>\n" );
document.write( "  <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=-37%2F28 ALIGN=MIDDLE  ALT=\"y=-37%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now plug this answer into the top equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax%2B36%2Ay=15 ALIGN=MIDDLE  ALT=\"8%2Ax%2B36%2Ay=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax%2B36%28-37%2F28%29=15 ALIGN=MIDDLE  ALT=\"8%2Ax%2B36%28-37%2F28%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-37%2F28 ALIGN=MIDDLE  ALT=\"y=-37%2F28\"   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=8%2Ax-1332%2F28=15 ALIGN=MIDDLE  ALT=\"8%2Ax-1332%2F28=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax-333%2F7=15 ALIGN=MIDDLE  ALT=\"8%2Ax-333%2F7=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax=15%2B333%2F7 ALIGN=MIDDLE  ALT=\"8%2Ax=15%2B333%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-333%2F7 ALIGN=MIDDLE  ALT=\"-333%2F7\"   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=8%2Ax=105%2F7%2B333%2F7 ALIGN=MIDDLE  ALT=\"8%2Ax=105%2F7%2B333%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make 15 into a fraction with a denominator of 7<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax=438%2F7 ALIGN=MIDDLE  ALT=\"8%2Ax=438%2F7\"   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%2F8%29%288%29%29%2Ax=%28438%2F7%29%281%2F8%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F8%29%288%29%29%2Ax=%28438%2F7%29%281%2F8%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%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left 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=x=219%2F28 ALIGN=MIDDLE  ALT=\"x=219%2F28\"   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( "  So our answer is <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=219%2F28 ALIGN=MIDDLE  ALT=\"x=219%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-37%2F28 ALIGN=MIDDLE  ALT=\"y=-37%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  which also looks like<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=219%2F28 ALIGN=MIDDLE  ALT=\"219%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-37%2F28 ALIGN=MIDDLE  ALT=\"-37%2F28\"   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=8%2Ax%2B36%2Ay=15 ALIGN=MIDDLE  ALT=\"8%2Ax%2B36%2Ay=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2B2%2Ay=13 ALIGN=MIDDLE  ALT=\"2%2Ax%2B2%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  we get <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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+-17.8214285714286%2C+17.8214285714286%2C+-11.3214285714286%2C+11.3214285714286%2C%0D%0A++++graph%28+500%2C+600%2C+-17.8214285714286%2C+17.8214285714286%2C+-11.3214285714286%2C+11.3214285714286%2C+%2815-8%2Ax%29%2F36%2C+%2813-2%2Ax%29%2F2+%29%2C%0D%0A++++blue%28++circle%28+7.82142857142857%2C+-1.32142857142857%2C+0.237619047619048+%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=8%2Ax%2B36%2Ay=15 ALIGN=MIDDLE  ALT=\"8%2Ax%2B36%2Ay=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2B2%2Ay=13 ALIGN=MIDDLE  ALT=\"2%2Ax%2B2%2Ay=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  and we can see that the two equations intersect at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=219%2F28 ALIGN=MIDDLE  ALT=\"219%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-37%2F28 ALIGN=MIDDLE  ALT=\"-37%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >). This verifies our answer.</TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, you can write your solution as decimal number like this:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.8 ALIGN=MIDDLE  ALT=\"7.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.3 ALIGN=MIDDLE  ALT=\"-1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );