document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381352>Question 381352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help? I need to graph a system of linear inequalities, then test to see what satisfies both. Here is the system:<BR>\n" );
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document.write( "                        x+y>4<BR>\n" );
document.write( "                        x+y<-1<BR>\n" );
document.write( "Here's what I have done so far:<BR>\n" );
document.write( "For Line 1, the first inequality:<BR>\n" );
document.write( "x-intercept is (4,0) and y-intercept is (0,4)\r<BR>\n" );
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document.write( "For Line 2, the second inequality:<BR>\n" );
document.write( "x-intercept is (-1,0) and y-intercept is (0,-1).\r<BR>\n" );
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document.write( "Ok, both these lines are dashed lines, since neither are equal, and therefore included, so I end up with two parallel dashed lines. My problem: I can't find an answer to satisfy BOTH inequalities, so I don't know what to shade in as \"true\".<BR>\n" );
document.write( "Can someone please set me straight and tell me what I am doing wrong? Thank you!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270476 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=270476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider this: Let z=x+y be some number\r<BR>\n" );
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document.write( "So the system \r<BR>\n" );
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document.write( "x+y>4<BR>\n" );
document.write( "x+y<-1\r<BR>\n" );
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document.write( "is really saying\r<BR>\n" );
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document.write( "z > 4<BR>\n" );
document.write( "z < -1\r<BR>\n" );
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document.write( "So the question is now: what number (z) is BOTH greater than 4 AND less than -1? This is impossible. Since no number exists, this means that there are no solutions to the system of inequalities above.\r<BR>\n" );
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document.write( "So there are no solutions to the system \r<BR>\n" );
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document.write( "x+y>4<BR>\n" );
document.write( "x+y<-1\r<BR>\n" );
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document.write( "Visually, you'll get the following\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/system_linear_ineq2.png\">\r<BR>\n" );
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document.write( "Where the blue shaded region refers to the solution set of x+y>4 and the red shaded region refers to the solution set of x+y<-1. Since the two regions will NEVER intersect (at any point in the xy plane), this means that the solution set is empty.\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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