document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82569>Question 82569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by addition:\r<BR>\n" );
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document.write( "-5x+2y=10<BR>\n" );
document.write( "x-3y=11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59157 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=59157\">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=-5%2Ax+%2B+2%2Ay+=+10 ALIGN=MIDDLE  ALT=\"-5%2Ax+%2B+2%2Ay+=+10\"   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+-3%2Ay+=+11 ALIGN=MIDDLE  ALT=\"1%2Ax+%2B+-3%2Ay+=+11\"   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 1 as our coefficient for x, to get  5 we have to multiply all terms of the second equation by <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;\" > which is equal to 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=%281%2A5%29x+%2B+%28-3%2A5%29y+=+11%2A5 ALIGN=MIDDLE  ALT=\"%281%2A5%29x+%2B+%28-3%2A5%29y+=+11%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ax+%2B+-15%2Ay+=+55 ALIGN=MIDDLE  ALT=\"5%2Ax+%2B+-15%2Ay+=+55\"   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=%28-5%2B5%29x+%2B+%282%2B-15%29y+=+%2810%2B55%29 ALIGN=MIDDLE  ALT=\"%28-5%2B5%29x+%2B+%282%2B-15%29y+=+%2810%2B55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since -5 and 5 cancel out, we have a linear equation:Therefore, we know that y = -5.<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=-5%2Ax+%2B+2%2Ay+=+10 ALIGN=MIDDLE  ALT=\"-5%2Ax+%2B+2%2Ay+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Ax+%2B+2%2A-5+=+10 ALIGN=MIDDLE  ALT=\"-5%2Ax+%2B+2%2A-5+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Ax+%2B+-10+=+10 ALIGN=MIDDLE  ALT=\"-5%2Ax+%2B+-10+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Ax+=+10+-+-10 ALIGN=MIDDLE  ALT=\"-5%2Ax+=+10+-+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+-+-10%29%2F-5 ALIGN=MIDDLE  ALT=\"x+=+%2810+-+-10%29%2F-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20%2F-5 ALIGN=MIDDLE  ALT=\"x+=+20%2F-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4 ALIGN=MIDDLE  ALT=\"x+=+-4\"   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=-4%2C+y=-5+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-4%2C+y=-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );