document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74108>Question 74108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.solve the system by addition.<BR>\n" );
document.write( "-2x+3y=-15<BR>\n" );
document.write( "x-2y=11\r<BR>\n" );
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document.write( "I got -x+y=-4 that doesn't seem right.\r<BR>\n" );
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document.write( "2.The difference of two numbers is 27. The second is 1 less than 3 times the first. What are the two numbers?\r<BR>\n" );
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document.write( "3.solve the following system of linear inequalities by graphing. <BR>\n" );
document.write( "3x+4y is less than or equal to 12<BR>\n" );
document.write( "x+3y is less than or equal to 6<BR>\n" );
document.write( "x is greater than or equal to 0<BR>\n" );
document.write( "y is greater than or equal to 0<BR>\n" );
document.write( "Sorry, i'm not sure how to show the lees than and greater than symbols.\r<BR>\n" );
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document.write( "I'd appreciate any help you could give me\r<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 #53098 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=53098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. <BR>\n" );
document.write( "You need to have either x or y have the same but opposite coefficients in order to eliminate them. <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "             -2x+3y=-15\r\n" );
document.write( "              2(x-2y)=2(11)     <--------Multiply both sides by 2\r\n" );
document.write( "                                    </PRE>\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "             -2x+3y=-15\r\n" );
document.write( "              2x-4y= 22     <--------Add the 2 equations\r\n" );
document.write( "         -----------------\r\n" );
document.write( "              0x -y=7\r\n" );
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document.write( "So y=-7 and x equals<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%28-7%29=11 ALIGN=MIDDLE  ALT=\"x-2%28-7%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11-14 ALIGN=MIDDLE  ALT=\"x=11-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "             -2(-3)+3(-7)=-15\r\n" );
document.write( "               (-3)-2(-7)=11     Plug in (-3,-7)\r\n" );
document.write( "                                    </PRE><BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "                   6+-21=-15\r\n" );
document.write( "               (-3)+14=11     Plug in (-3,-7)\r\n" );
document.write( "                                    </PRE><BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "                   -15=-15            Works\r\n" );
document.write( "                    11=11             Works\r\n" );
document.write( "                                    </PRE><BR>\n" );
document.write( "So (-3,-7) is the solution.\r<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( "Let f=1st # and s=2nd #<BR>\n" );
document.write( "Here's the translated word problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s-f=27 ALIGN=MIDDLE  ALT=\"s-f=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"difference of two numbers is (=) 27\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=3f-1 ALIGN=MIDDLE  ALT=\"s=3f-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"second (s) is (=) 1 less (-) than 3 times the first (3f)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=27%2Bf ALIGN=MIDDLE  ALT=\"s=27%2Bf\"   DISABLED_style= \"max-width:90%; height:auto;\" >Solve for s, plug this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=3f-1 ALIGN=MIDDLE  ALT=\"s=3f-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2Bf=3f-1 ALIGN=MIDDLE  ALT=\"27%2Bf=3f-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28=2f ALIGN=MIDDLE  ALT=\"28=2f\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=14 ALIGN=MIDDLE  ALT=\"f=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the 1st number is 7 the 2nd number is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=27%2B14 ALIGN=MIDDLE  ALT=\"s=27%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=41 ALIGN=MIDDLE  ALT=\"s=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<p><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41-14=27 ALIGN=MIDDLE  ALT=\"41-14=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27=27 ALIGN=MIDDLE  ALT=\"27=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >works<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41=3%2814%29-1 ALIGN=MIDDLE  ALT=\"41=3%2814%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41=41 ALIGN=MIDDLE  ALT=\"41=41\"   DISABLED_style= \"max-width:90%; height:auto;\" >works\r<BR>\n" );
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document.write( "3.<BR>\n" );
document.write( "To solve the system graphically, we need to graph the inequalities. To do this we must make them an equation and solve for y<BR>\n" );
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;\" >Solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=12 ALIGN=MIDDLE  ALT=\"3x%2B4y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >Make an equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=12-3x ALIGN=MIDDLE  ALT=\"4y=12-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 3x from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-%283%2F4%29x ALIGN=MIDDLE  ALT=\"y=3-%283%2F4%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >Divide both sides by 4. Now we can graph this equation<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;\" >Solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=6 ALIGN=MIDDLE  ALT=\"x%2B3y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Make an equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=6-x ALIGN=MIDDLE  ALT=\"3y=6-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract x from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2-%281%2F3%29x ALIGN=MIDDLE  ALT=\"y=2-%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >Divide both sides by 3. Now we can graph this equation<BR>\n" );
document.write( "Since x and y is greater than x, we only need to graph these equations in the 1st quadrant (the upper left portion of the graph). So the graphs look like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+0%2C+7%2C+0%2C+10%2C+2-%281%2F3%29x%2C+3-%283%2F4%29x%29+ ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+0%2C+7%2C+0%2C+10%2C+2-%281%2F3%29x%2C+3-%283%2F4%29x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To complete this we need to test which points will satisfy this set of inequalities. Let's try (0,0) plug this into <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%280%29%2B4%280%29%3C=12 ALIGN=MIDDLE  ALT=\"3%280%29%2B4%280%29%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=12 ALIGN=MIDDLE  ALT=\"0%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which is true<BR>\n" );
document.write( "Now try (0,0), plug this into <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B3%280%29%3C=6 ALIGN=MIDDLE  ALT=\"0%2B3%280%29%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=6 ALIGN=MIDDLE  ALT=\"0%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which is true. This means you shade the region that contains (0,0) for both inequalities, which is below the graph for both. Since these regions overlap, you would ultimately shade their overlapping region, which is bounded by the x and y axises and the lines. If you want a picture email me and I'll send you one to give you an idea of what it looks like. Hope this helps. </SPAN>\n" );
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