document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79778>Question 79778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of equations using the addition (elimination) method. Be sure to state the solution to the system.<BR>\n" );
document.write( "x+2y=-7<BR>\n" );
document.write( "2x+3y=-12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57237 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=57237\">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=change_this_name6744.solver>Linear Systems by Addition</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>We'll solve the system:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+%2B+2%2Ay+=+-7 ALIGN=MIDDLE  ALT=\"1%2Ax+%2B+2%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=2%2Ax+%2B+3%2Ay+=+-12 ALIGN=MIDDLE  ALT=\"2%2Ax+%2B+3%2Ay+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  by elimination by addition.To eliminate by addition, we need to set both coefficients of x to numbers with changed signs, i.e a and -a. Since in the second equation we have 2 as our coefficient for x, to get  -1 we have to multiply all terms of the second equation 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;\" > which is equal to -0.5.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Multiplying, we get on our second equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A-0.5%29x+%2B+%283%2A-0.5%29y+=+-12%2A-0.5 ALIGN=MIDDLE  ALT=\"%282%2A-0.5%29x+%2B+%283%2A-0.5%29y+=+-12%2A-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Ax+%2B+-1.5%2Ay+=+6 ALIGN=MIDDLE  ALT=\"-1%2Ax+%2B+-1.5%2Ay+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Adding both equations we get:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B-1%29x+%2B+%282%2B-1.5%29y+=+%28-7%2B6%29 ALIGN=MIDDLE  ALT=\"%281%2B-1%29x+%2B+%282%2B-1.5%29y+=+%28-7%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since 1 and -1 cancel out, we have a linear equation:Therefore, we know that y = -2.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plugging that in into the first equation gives us:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+%2B+2%2Ay+=+-7 ALIGN=MIDDLE  ALT=\"1%2Ax+%2B+2%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=1%2Ax+%2B+2%2A-2+=+-7 ALIGN=MIDDLE  ALT=\"1%2Ax+%2B+2%2A-2+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+%2B+-4+=+-7 ALIGN=MIDDLE  ALT=\"1%2Ax+%2B+-4+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+=+-7+-+-4 ALIGN=MIDDLE  ALT=\"1%2Ax+=+-7+-+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+-+-4%29%2F1 ALIGN=MIDDLE  ALT=\"x+=+%28-7+-+-4%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F1 ALIGN=MIDDLE  ALT=\"x+=+-3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Therefore, our answer is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=-3%2C+y=-2+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-3%2C+y=-2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So the solution is (-3,-2) </SPAN>\n" );
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