document.write( "Question 60771: How can I solve the following system of linear inequalities by graphing.
\n" ); document.write( " 3x – y < 2
\n" ); document.write( " x + y > 2
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Algebra.Com's Answer #41742 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
How can I solve the following system of linear inequalities by graphing.\r\n" );
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document.write( "        3x – y < 2\r\n" );
document.write( "         x + y > 2\r\n" );
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document.write( "First form the equations of the boundary lines, graphing one at a\r\n" );
document.write( "time. To form them replace the inequalities by = signs\r\n" );
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document.write( "        3x – y = 2\r\n" );
document.write( "         x + y = 2\r\n" );
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document.write( "Graph the first one by getting two points, say,  (0, -2) and (2, 4)\r\n" );
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document.write( "        \r\n" );
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document.write( "That line should be a dotted line, not a solid line,\r\n" );
document.write( "since it's \" < \" and not \" < \", but I can't do that on here, \r\n" );
document.write( "but you can on your paper.\r\n" );
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document.write( "Now before graphing the second one, pick any arbirtary point\r\n" );
document.write( "that you are sure is not on that line as a test point.\r\n" );
document.write( "Say we pick  (x,y) = (-2,4) and substitute that in the\r\n" );
document.write( "first original inequality to see whether it is true or false\r\n" );
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document.write( "        3x – y < 2\r\n" );
document.write( "     3(-2) - 4 < 2\r\n" );
document.write( "        -6 - 4 < 2\r\n" );
document.write( "           -10 < 2\r\n" );
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document.write( "This is true so the part we will shade has got to be on the \r\n" );
document.write( "SAME side of that line as the test point we chose, (-2,4).\r\n" );
document.write( "Since (-2,4) is above and to the left of the line, the region \r\n" );
document.write( "we will shade will be above and to the left of that line\r\n" );
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document.write( "Now graph the second bondary line by getting two points, say,\r\n" );
document.write( "(0, 2) and (2, 0). Graph it on the same set of axes:\r\n" );
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document.write( "        \r\n" );
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document.write( "That one should be dotted too, since it's \" > \" and not \" > \"\r\n" );
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document.write( "Now pick any arbirtary point that you are sure is not on that\r\n" );
document.write( "line as a test point.\r\n" );
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document.write( "Say we pick  (x,y) = (-6,2) and substitute that in the\r\n" );
document.write( "second original inequality to see whether it is true or false\r\n" );
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document.write( "         x + y > 2\r\n" );
document.write( "        -2 + 2 > 2\r\n" );
document.write( "             0 > 2\r\n" );
document.write( "             0 > 2\r\n" );
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document.write( "This is false so the region we will shade has got to be on the \r\n" );
document.write( "OPPOSITE side of that line as the test point we chose, (-6,2).\r\n" );
document.write( "Since (-6,2) is below and to the left of the second line, the \r\n" );
document.write( "region we will shade will be above and to the right of that line.\r\n" );
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document.write( "So the region we will shade is the upper V-shaped wedge which\r\n" );
document.write( "is above and to the left of the red line and above and to the\r\n" );
document.write( "left of the green line. \r\n" );
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document.write( "I can't shade on here but you can on your paper, and remember\r\n" );
document.write( "to draw both lines dotted.\r\n" );
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document.write( "Edwin
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