document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173706>Question 173706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to solve. I'm having trouble understanding from when I asked a few days ago.\r<BR>\n" );
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document.write( "Solve by graphing. <BR>\n" );
document.write( "3x + 4y &#8804; 12<BR>\n" );
document.write( "x + 3y &#8804; 6<BR>\n" );
document.write( "x &#8805; 0<BR>\n" );
document.write( "y &#8805; 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128625 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve by graphing.<BR>\n" );
document.write( "3x + 4y &#8804; 12<BR>\n" );
document.write( "x + 3y &#8804; 6<BR>\n" );
document.write( "x &#8805; 0<BR>\n" );
document.write( "y &#8805; 0\r<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "Plot the 1st two equations, put the equations in the slope/intercept form<BR>\n" );
document.write( "3x + 4y =< 12<BR>\n" );
document.write( "4y = 12 - 3x<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F4 ALIGN=MIDDLE  ALT=\"12%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 3<BR>\n" );
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document.write( "Calculate two points (substitute the values for x and find y):<BR>\n" );
document.write( " x | y<BR>\n" );
document.write( "-------<BR>\n" );
document.write( " 0 | 4<BR>\n" );
document.write( " 4 | 1<BR>\n" );
document.write( "Graph should look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+5%2C+-4%2C+6%2C+-.75x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+5%2C+-4%2C+6%2C+-.75x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the same with the 2nd equation<BR>\n" );
document.write( "x + 3y => 6<BR>\n" );
document.write( "3y = 6 - x<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F3 ALIGN=MIDDLE  ALT=\"6%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F3 ALIGN=MIDDLE  ALT=\"x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2<BR>\n" );
document.write( "Calculate two points (substitute the values for x and find y):<BR>\n" );
document.write( " x | y<BR>\n" );
document.write( "-------<BR>\n" );
document.write( " 0 | 2<BR>\n" );
document.write( " 3 | 1<BR>\n" );
document.write( "Graph should look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+5%2C+-4%2C+6%2C+-.33x%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+5%2C+-4%2C+6%2C+-.33x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The last two equations tell you that only positive values for x and y are considered<BR>\n" );
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document.write( "Put both graphs on the same coordinate system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+5%2C+-4%2C+6%2C+-.75x%2B4%2C+-.33x%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+5%2C+-4%2C+6%2C+-.75x%2B4%2C+-.33x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Look at this graph<BR>\n" );
document.write( "The 1st equation:3x + 4y =< ; 12, the purple line<BR>\n" );
document.write( "Area of feasibility is at or below this line<BR>\n" );
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document.write( "The 2nd equation: x + 3y => 6, green line<BR>\n" );
document.write( "Area of feasibility is at or above this line<BR>\n" );
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document.write( "x => 0<BR>\n" );
document.write( "y => 0<BR>\n" );
document.write( "As I said before, this means only positive values for x & y, inside the area of feasibility are considered.<BR>\n" );
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document.write( "The solution is the triangular area between the lines and to the right of the y axis.   </SPAN>\n" );
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