document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=414112>Question 414112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the solution of the system? Solve the system by the elimination.<BR>\n" );
document.write( "5x+5y=-7<BR>\n" );
document.write( "7x-3y=17 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290456 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=290456\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B5y=-7 ALIGN=MIDDLE  ALT=\"5x%2B5y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-3y=17 ALIGN=MIDDLE  ALT=\"7x-3y=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<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_elimination.solver>Solving a System of Linear Equations by Elimination/Addition</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=5%2Ax%2B5%2Ay=-7 ALIGN=MIDDLE  ALT=\"5%2Ax%2B5%2Ay=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Ax-3%2Ay=17 ALIGN=MIDDLE  ALT=\"7%2Ax-3%2Ay=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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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" );
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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 5 and 7 to some equal number, we could try to get them to the LCM.<BR>\n" );
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document.write( "  Since the LCM of 5 and 7 is 35, we need to multiply both sides of the top equation by 7 and multiply both sides of the bottom equation by -5 like this:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A%285%2Ax%2B5%2Ay%29=%28-7%29%2A7 ALIGN=MIDDLE  ALT=\"7%2A%285%2Ax%2B5%2Ay%29=%28-7%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the top equation (both sides) by 7<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2A%287%2Ax-3%2Ay%29=%2817%29%2A-5 ALIGN=MIDDLE  ALT=\"-5%2A%287%2Ax-3%2Ay%29=%2817%29%2A-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the bottom equation (both sides) by -5<BR>\n" );
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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=35%2Ax%2B35%2Ay=-49 ALIGN=MIDDLE  ALT=\"35%2Ax%2B35%2Ay=-49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-35%2Ax%2B15%2Ay=-85 ALIGN=MIDDLE  ALT=\"-35%2Ax%2B15%2Ay=-85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Notice how 35 and -35 add to zero (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2B-35=0 ALIGN=MIDDLE  ALT=\"35%2B-35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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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=%2835%2Ax-35%2Ax%29%2B%2835%2Ay%2B15%2Ay%29=-49-85 ALIGN=MIDDLE  ALT=\"%2835%2Ax-35%2Ax%29%2B%2835%2Ay%2B15%2Ay%29=-49-85\"   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=%2835-35%29%2Ax%2B%2835%2B15%29y=-49-85 ALIGN=MIDDLE  ALT=\"%2835-35%29%2Ax%2B%2835%2B15%29y=-49-85\"   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%2835%2B-35%29%2Ax%2B%2835%2B15%29%2Ay=-49-85 ALIGN=MIDDLE  ALT=\"cross%2835%2B-35%29%2Ax%2B%2835%2B15%29%2Ay=-49-85\"   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" );
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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=50%2Ay=-134 ALIGN=MIDDLE  ALT=\"50%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=y=-134%2F50 ALIGN=MIDDLE  ALT=\"y=-134%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   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=-67%2F25 ALIGN=MIDDLE  ALT=\"y=-67%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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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=5%2Ax%2B5%2Ay=-7 ALIGN=MIDDLE  ALT=\"5%2Ax%2B5%2Ay=-7\"   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=5%2Ax%2B5%28-67%2F25%29=-7 ALIGN=MIDDLE  ALT=\"5%2Ax%2B5%28-67%2F25%29=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-67%2F25 ALIGN=MIDDLE  ALT=\"y=-67%2F25\"   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=5%2Ax-335%2F25=-7 ALIGN=MIDDLE  ALT=\"5%2Ax-335%2F25=-7\"   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=5%2Ax-67%2F5=-7 ALIGN=MIDDLE  ALT=\"5%2Ax-67%2F5=-7\"   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=5%2Ax=-7%2B67%2F5 ALIGN=MIDDLE  ALT=\"5%2Ax=-7%2B67%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-67%2F5 ALIGN=MIDDLE  ALT=\"-67%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=5%2Ax=-35%2F5%2B67%2F5 ALIGN=MIDDLE  ALT=\"5%2Ax=-35%2F5%2B67%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make -7 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=5%2Ax=32%2F5 ALIGN=MIDDLE  ALT=\"5%2Ax=32%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%2F5%29%285%29%29%2Ax=%2832%2F5%29%281%2F5%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F5%29%285%29%29%2Ax=%2832%2F5%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 ALIGN=MIDDLE  ALT=\"5\"   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=32%2F25 ALIGN=MIDDLE  ALT=\"x=32%2F25\"   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( "  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=32%2F25 ALIGN=MIDDLE  ALT=\"x=32%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-67%2F25 ALIGN=MIDDLE  ALT=\"y=-67%2F25\"   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=32%2F25 ALIGN=MIDDLE  ALT=\"32%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-67%2F25 ALIGN=MIDDLE  ALT=\"-67%2F25\"   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=5%2Ax%2B5%2Ay=-7 ALIGN=MIDDLE  ALT=\"5%2Ax%2B5%2Ay=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Ax-3%2Ay=17 ALIGN=MIDDLE  ALT=\"7%2Ax-3%2Ay=17\"   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+-11.28%2C+11.28%2C+-12.68%2C+12.68%2C%0D%0A++++graph%28+500%2C+600%2C+-11.28%2C+11.28%2C+-12.68%2C+12.68%2C+%28-7-5%2Ax%29%2F5%2C+%2817-7%2Ax%29%2F-3+%29%2C%0D%0A++++blue%28++circle%28+1.28%2C+-2.68%2C+0.1504+%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=5%2Ax%2B5%2Ay=-7 ALIGN=MIDDLE  ALT=\"5%2Ax%2B5%2Ay=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Ax-3%2Ay=17 ALIGN=MIDDLE  ALT=\"7%2Ax-3%2Ay=17\"   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=32%2F25 ALIGN=MIDDLE  ALT=\"32%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-67%2F25 ALIGN=MIDDLE  ALT=\"-67%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >). This verifies our answer.</TD></TR>\n" );
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