document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935059>Question 935059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The system of inequalities below has exactly N solutions of the form (a, b), where a and b are positive integers. Find the value of N.<BR>\n" );
document.write( "x+3y is less than or equal to 30<BR>\n" );
document.write( "3x+y is less than or equal to 30<BR>\n" );
document.write( "I am sorry I can't put in the \"lesser than or equal to\" sign, but I hope what I did is understandable. I got 67, but I am probably wrong. Thanks again.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568173 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39627)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=568173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+3y<=30 and 3x+y<=30, and then surround each inequality with triple left and triple right curly braces<BR>\n" );
document.write( "for rendering purposes.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y%3C=30 ALIGN=MIDDLE  ALT=\"x%2B3y%3C=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%3C=-x%2B30 ALIGN=MIDDLE  ALT=\"3y%3C=-x%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-x%2F3%2B10 ALIGN=MIDDLE  ALT=\"y%3C=-x%2F3%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By%3C=30 ALIGN=MIDDLE  ALT=\"3x%2By%3C=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-3x%2B30 ALIGN=MIDDLE  ALT=\"y%3C=-3x%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The system can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y%3C=-x%2F3%2B10%2Cy%3C=-3x%2B30%29 ALIGN=MIDDLE  ALT=\"system%28y%3C=-x%2F3%2B10%2Cy%3C=-3x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You graph each line and then use the inequality statements to show which region of points<BR>\n" );
document.write( "satisfies BOTH statements.  (I have not figured out yet how to make the graph properly render<BR>\n" );
document.write( "to show this type of graphed system of inequalities.)\r<BR>\n" );
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document.write( "This graph is not complete:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28-12%2C12%2C0%2C35%2C-x%2F3%2B10%2C-3x%2B30%29 ALIGN=MIDDLE  ALT=\"graph%28-12%2C12%2C0%2C35%2C-x%2F3%2B10%2C-3x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In fact, the entire graph code rendering is failing, so you probably see nothing there.<BR>\n" );
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