document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28678>Question 28678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  Solve the following system of linear inequalities by graphing.<BR>\n" );
document.write( "	x + 2y <= 3<BR>\n" );
document.write( "	2x – 3y <= 6\r<BR>\n" );
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document.write( "2.  Solve the following system of linear inequalities by graphing.<BR>\n" );
document.write( "	  3x + 4y <=12<BR>\n" );
document.write( "	    x + 3y <= 6<BR>\n" );
document.write( "	             x => 0<BR>\n" );
document.write( "		 y => 0\r<BR>\n" );
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document.write( "Please help!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15636 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, plot or sketch the first 2 straight lines:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C10%2C-2%2C6%2C%28-3%2F4%29x%2B3%2C+%28-1%2F3%29x%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C10%2C-2%2C6%2C%28-3%2F4%29x%2B3%2C+%28-1%2F3%29x%2B2%29\"   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%2B4y+%3C=+12 ALIGN=MIDDLE  ALT=\"3x%2B4y+%3C=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the brown line, also quoted as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+%28-3%2F4%29x+%2B+3 ALIGN=MIDDLE  ALT=\"y+%3C=+%28-3%2F4%29x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y+%3C=+6 ALIGN=MIDDLE  ALT=\"x%2B3y+%3C=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the green line, also quoted as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+%28-1%2F3%29x+%2B+2 ALIGN=MIDDLE  ALT=\"y+%3C=+%28-1%2F3%29x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, for the first equation... pick a point that is NOT on the line. And pick a nice easy point ie one with small numbers...i choose the origin (0,0).\r<BR>\n" );
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document.write( "y and  (-3/4)x + 3<BR>\n" );
document.write( "--> 0 and (-3/4)(0) + 3<BR>\n" );
document.write( "--> 0 and 0 + 3<BR>\n" );
document.write( "--> 0 and 3<BR>\n" );
document.write( "--> zero is less than 3<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+%28-3%2F4%29x+%2B+3 ALIGN=MIDDLE  ALT=\"y+%3C=+%28-3%2F4%29x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the region below the line... SHADE EVERYTHING ABOVE THE LINE, as this is NOT wanted.\r<BR>\n" );
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document.write( "Repeat for the second line, and pick a point, again i pick (0,0):<BR>\n" );
document.write( "y and (-1/3)x + 2<BR>\n" );
document.write( "--> 0 and (-1/3)(0) + 2<BR>\n" );
document.write( "--> 0 and 0+2<BR>\n" );
document.write( "--> 0 and 2<BR>\n" );
document.write( "--> zero is LESS than 2<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+%28-1%2F3%29x+%2B+2 ALIGN=MIDDLE  ALT=\"y+%3C=+%28-1%2F3%29x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the region below that line... SHADE EVERYTHING ABOVE THE LINE, as this is NOT wanted.\r<BR>\n" );
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document.write( "And now, the third line, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Well x=0 is the y-axis. And we want every point/place on the graph that is greater or equal to that line...this is everything to the right of the y-axis. SHADE EVERYTHING TO THE LEFT OF THE y-axis, as this is NOT wanted.\r<BR>\n" );
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document.write( "And now, the last line, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E=+0 ALIGN=MIDDLE  ALT=\"y+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Well, y=0 is the x-axis. And we want every point/place on the graph that is greater or equal to that line... this is everything above the x-axis. SHADE EVERYTHING BELOW THE x-axis, as this is NOT wanted.\r<BR>\n" );
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document.write( "What region is left clear? is is the little 4-sided shape in the middle, bounded by the x- and y-axis and the 2 straight lines forming a ^ shape.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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