document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=382793>Question 382793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph this system of inequalities\r<BR>\n" );
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document.write( "{9x^2+25y^2<=225<BR>\n" );
document.write( "{x^2+4y^2>=16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #271236 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=271236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2%2B25y%5E2=225 ALIGN=MIDDLE  ALT=\"9x%5E2%2B25y%5E2=225\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you get an ellipse.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C+sqrt%28%28225-9x%5E2%29%2F25%29%29%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-sqrt%28%28225-9x%5E2%29%2F25%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you pick a point (0,0) and test the inequality.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B0%3C=225 ALIGN=MIDDLE  ALT=\"0%2B0%3C=225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution region is the area inside of the ellipse.<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=plot_any_inequality.solver>Plot Any Inequality</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Graphing function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2%2B25y%5E2%3C=225 ALIGN=MIDDLE  ALT=\"9x%5E2%2B25y%5E2%3C=225\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+9x%5E2%2B25y%5E2%3C=225+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+9x%5E2%2B25y%5E2%3C=225+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Similarly if you graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4y%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2%2B4y%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you also get an ellipse.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C+sqrt%28%2816-x%5E2%29%2F4%29%29%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-sqrt%28%2816-x%5E2%29%2F4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you pick a point (0,0) and test the inequality.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B0%3E=225 ALIGN=MIDDLE  ALT=\"0%2B0%3E=225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution region is the area outside of the ellipse.<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=plot_any_inequality.solver>Plot Any Inequality</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Graphing function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4y%5E2%3E=16 ALIGN=MIDDLE  ALT=\"x%5E2%2B4y%5E2%3E=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B4y%5E2%3E=16+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B4y%5E2%3E=16+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So for the system of equations the solution region would be the area between the two ellipses, outside the smaller one and inside the larger one.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C0%2C+sqrt%28%2816-x%5E2%29%2F4%29%29%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C0%2C+-sqrt%28%2816-x%5E2%29%2F4%29%29%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C+sqrt%28%28225-9x%5E2%29%2F25%29%29%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-sqrt%28%28225-9x%5E2%29%2F25%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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