document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=650141>Question 650141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of inequalities by graphing. draw a graph<BR>\n" );
document.write( "5x - 4y &#8805; -20<BR>\n" );
document.write( "3x - 2y &#8804; -8<BR>\n" );
document.write( "y &#8805; -3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-9x + 6y &#8805; 18<BR>\n" );
document.write( "-x + 3y &#8805; -12<BR>\n" );
document.write( "y &#8804; 4	<BR>\n" );
document.write( "	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3x + 12y &#8805; -108<BR>\n" );
document.write( "-7x + 6y &#8804; 48<BR>\n" );
document.write( "y &#8804; -4<BR>\n" );
document.write( "	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "6x + 10y &#8804; -40<BR>\n" );
document.write( "x + y &#8804; -8	<BR>\n" );
document.write( "y &#8805; -1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4x + 16y &#8805; 128	<BR>\n" );
document.write( "-3x + 8y &#8804; 80<BR>\n" );
document.write( "y &#8804; 12<BR>\n" );
document.write( "	\r<BR>\n" );
document.write( "\n" );
document.write( "3x + 9y < -18<BR>\n" );
document.write( "-x + 3y &#8804; 12<BR>\n" );
document.write( "y < 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5x + 2y &#8805; -6	<BR>\n" );
document.write( "-5x + 2y < 14	<BR>\n" );
document.write( "y < 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-6x - 2y < -16	<BR>\n" );
document.write( "2x - y > 2	<BR>\n" );
document.write( "y &#8805; -4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407203 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=407203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First you have to solve the first one for y and put it into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > form, but remember to switch the sign if you divide by -1 \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+-+4y+%3E=+-20 ALIGN=MIDDLE  ALT=\"5x+-+4y+%3E=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-+2y+%3C=+-8 ALIGN=MIDDLE  ALT=\"3x+-+2y+%3C=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E=+-3 ALIGN=MIDDLE  ALT=\"y+%3E=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+-+4y+%3E=+-20 ALIGN=MIDDLE  ALT=\"5x+-+4y+%3E=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >..->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B20%3E=+4y ALIGN=MIDDLE  ALT=\"5x+%2B20%3E=+4y\"   DISABLED_style= \"max-width:90%; height:auto;\" >->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F4%29x+%2B5%3E=+y ALIGN=MIDDLE  ALT=\"%285%2F4%29x+%2B5%3E=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >...or ..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=%285%2F4%29x+%2B5 ALIGN=MIDDLE  ALT=\"y%3C=%285%2F4%29x+%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-+2y+%3C=+-8 ALIGN=MIDDLE  ALT=\"3x+-+2y+%3C=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >..->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B8%3E=+2y ALIGN=MIDDLE  ALT=\"3x+%2B8%3E=+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29x+%2B4%3E=+y ALIGN=MIDDLE  ALT=\"%283%2F2%29x+%2B4%3E=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >...or...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=%283%2F2%29x+%2B4 ALIGN=MIDDLE  ALT=\"y%3C=%283%2F2%29x+%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E=+-3 ALIGN=MIDDLE  ALT=\"y+%3E=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "\"Solving\" systems of linear inequalities means \"graphing each individual inequality, and then finding the overlaps of the various solutions\". <BR>\n" );
document.write( "So you need to graph each inequality, and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=find ALIGN=MIDDLE  ALT=\"find\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=overlapping ALIGN=MIDDLE  ALT=\"overlapping\"   DISABLED_style= \"max-width:90%; height:auto;\" > portions of the solution regions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "first see them just like lines\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-20%2C+15%2C+-20%2C+15%2C%283%2F2%29x+%2B4%2C%285%2F4%29x+%2B5%2C+y=-3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now see overlapping area (on this picture painted white)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-20%2C+15%2C+-20%2C+15%2Cy%3C=%283%2F2%29x+%2B4%2Cy%3C=%285%2F4%29x+%2B5%2C+y%3E=-3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "2.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x+%2B+6y+%3E=+18 ALIGN=MIDDLE  ALT=\"-9x+%2B+6y+%3E=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+3y+%3E=+-12 ALIGN=MIDDLE  ALT=\"-x+%2B+3y+%3E=+-12\"   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=+4 ALIGN=MIDDLE  ALT=\"y+%3C=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x+%2B+6y+%3E=+18 ALIGN=MIDDLE  ALT=\"-9x+%2B+6y+%3E=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >..->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y%3E=9x%2B18 ALIGN=MIDDLE  ALT=\"6y%3E=9x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" >->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=%289%2F6%29x%2B3 ALIGN=MIDDLE  ALT=\"y%3E=%289%2F6%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+3y+%3E=+-12 ALIGN=MIDDLE  ALT=\"-x+%2B+3y+%3E=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >}..->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%3E=x%2B12 ALIGN=MIDDLE  ALT=\"3y%3E=x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >..->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=%281%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3E=%281%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+4 ALIGN=MIDDLE  ALT=\"y+%3C=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+25%2C+-5%2C+25%2C%289%2F6%29x%2B3%2C%281%2F3%29x%2B4%2C+y=4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now see overlapping area (on this picture painted white)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+25%2C+-5%2C+25%2Cy%3E=%289%2F6%29x%2B3%2Cy%3E=%281%2F3%29x%2B4%2C+y+%3C=+4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "I hope, you will be able to solve other systems by yourself following these examples.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );