document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083513>Question 1083513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that -3 <= 7x + 2y <= 3 and -4 <= y - x <= 4$, what is the maximum possible value of x + y?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697519 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The solution to each (compound) inequality can be graphed as<BR>\n" );
document.write( "2 parallel lines, and all the (x,y) points in between.<BR>\n" );
document.write( "The solution to the whole system is a parallelogram including its sides.<BR>\n" );
document.write( "Point (0,0) is included in the parallelogram.<BR>\n" );
document.write( "The lines x+y=constant are parallel to each other,<BR>\n" );
document.write( "but not parallel to any side of the parallelogram,<BR>\n" );
document.write( "So, one of them will just touch one vertex.<BR>\n" );
document.write( "The sum x+y at that point is the maximum.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-5%2C5%2C5%2C-5%29%2Cline%28-5%2C8%2C5%2C-2%29%2C%0D%0Alocate%28-4.5%2C3%2Cx%2By=0%29%2Clocate%281%2C2.5%2Cx%2By=3%29%2C%0D%0Agraph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Ax%2B4%2Cx-4%2C%283-7x%29%2F2%2C-%283%2B7x%29%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That vertex must be the intersection of boundary lines<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B2y=3 ALIGN=MIDDLE  ALT=\"7x%2B2y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B4 ALIGN=MIDDLE  ALT=\"y=x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x=4 ALIGN=MIDDLE  ALT=\"y-x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substituting, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B2%28x%2B4%29=3 ALIGN=MIDDLE  ALT=\"7x%2B2%28x%2B4%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B2x%2B8=3 ALIGN=MIDDLE  ALT=\"7x%2B2x%2B8=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x=-5 ALIGN=MIDDLE  ALT=\"9x=-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=-5%2F9 ALIGN=MIDDLE  ALT=\"x=-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%2F9%2B4=31%2F9 ALIGN=MIDDLE  ALT=\"y=-5%2F9%2B4=31%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=-5%2F9%2B31%2F9=26%2F9=2%268%2F9 ALIGN=MIDDLE  ALT=\"x%2By=-5%2F9%2B31%2F9=26%2F9=2%268%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Just graph the lines, and check my calculations. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );