document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82041>Question 82041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistaent or dependent:\r<BR>\n" );
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document.write( "2x+3y=1<BR>\n" );
document.write( "5x+3y=16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58767 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=58767\">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=2%2Ax+%2B+3%2Ay+=+1 ALIGN=MIDDLE  ALT=\"2%2Ax+%2B+3%2Ay+=+1\"   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+3%2Ay+=+16 ALIGN=MIDDLE  ALT=\"5%2Ax+%2B+3%2Ay+=+16\"   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 5 as our coefficient for x, to get  -2 we have to multiply all terms of the second equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F5 ALIGN=MIDDLE  ALT=\"-2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equal to -0.4.<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=%285%2A-0.4%29x+%2B+%283%2A-0.4%29y+=+16%2A-0.4 ALIGN=MIDDLE  ALT=\"%285%2A-0.4%29x+%2B+%283%2A-0.4%29y+=+16%2A-0.4\"   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+-1.2%2Ay+=+-6.4 ALIGN=MIDDLE  ALT=\"-2%2Ax+%2B+-1.2%2Ay+=+-6.4\"   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=%282%2B-2%29x+%2B+%283%2B-1.2%29y+=+%281%2B-6.4%29 ALIGN=MIDDLE  ALT=\"%282%2B-2%29x+%2B+%283%2B-1.2%29y+=+%281%2B-6.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since 2 and -2 cancel out, we have a linear equation:Therefore, we know that y = -3.<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=2%2Ax+%2B+3%2Ay+=+1 ALIGN=MIDDLE  ALT=\"2%2Ax+%2B+3%2Ay+=+1\"   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%2A-3+=+1 ALIGN=MIDDLE  ALT=\"2%2Ax+%2B+3%2A-3+=+1\"   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+-9+=+1 ALIGN=MIDDLE  ALT=\"2%2Ax+%2B+-9+=+1\"   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+=+1+-+-9 ALIGN=MIDDLE  ALT=\"2%2Ax+=+1+-+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281+-+-9%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%281+-+-9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%2F2 ALIGN=MIDDLE  ALT=\"x+=+10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   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=5%2C+y=-3+%29 ALIGN=MIDDLE  ALT=\"system%28+x=5%2C+y=-3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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