document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112964>Question 112964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> three times the sum of two numbers exceeds twice their difference by five, while half the sum is two more than the difference. what are the two numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82290 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the numbers be x and y<BR>\n" );
document.write( "A) 3(x+y)=2(x-y)+5<BR>\n" );
document.write( "B) (x+y)/2=x-y+2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A) 3x+3y=2x-2y+5<BR>\n" );
document.write( "x+5y=5<BR>\n" );
document.write( "B)x+y=2x-2y+4 multiply both sides by 2.<BR>\n" );
document.write( "-x+3y=4<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=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cx+%2B+5%5Cy+=+5%2C%0D%0A++++-1%5Cx+%2B+3%5Cy+=+4+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+5%5Cy+=+5%2C%0D%0A++++-1%5Cx+%2B+3%5Cy+=+4+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 5*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+=+5+-+5%2Ay ALIGN=MIDDLE  ALT=\"1%2Ax+=+5+-+5%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F1+-+5%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+5%2F1+-+5%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%285%2F1+-+5%2Ay%2F1%29+%2B+3%5Cy+=+4 ALIGN=MIDDLE  ALT=\"-1%2A%285%2F1+-+5%2Ay%2F1%29+%2B+3%5Cy+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=1.125. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F1+-+5%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+5%2F1+-+5%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=-0.625.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=-0.625%2C+y=1.125+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-0.625%2C+y=1.125+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "A)<BR>\n" );
document.write( "3(-.625+1.125)=1.5<BR>\n" );
document.write( "2(-6.25+1.125)=-3.5 difference of 5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "B)<BR>\n" );
document.write( "(-.625+1.125)/2=.25<BR>\n" );
document.write( "-.625-1.125=-1.75 difference of 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed<BR>\n" );
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