document.write( "Question 1153833: Show graphically the solution set for the linear inequalities.
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Algebra.Com's Answer #776146 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\"system%28x+%2B+y+%3C=+4%2C%0D%0A2x+-+y+%3C=+4%29\"\r\n" );
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document.write( "First graph the boundary lines, one at a time, which are the lines whose\r\n" );
document.write( "equations are just like the inequalities with the symbols of inequality changed\r\n" );
document.write( "to symbols of equality (\"=\").\r\n" );
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document.write( "\"system%28x+%2B+y+=+4%2C%0D%0A2x+-+y+=+4%29\"\r\n" );
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document.write( "We graph the first boundary line (in green), x + y = 4, which has intercepts\r\n" );
document.write( "(0,4) and (4,0)\r\n" );
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document.write( "Before we draw the other boundary line, let's find out which side of the line\r\n" );
document.write( "all the solutions to the inequality x + y ≤ 4 are on.  We do that by\r\n" );
document.write( "substituting any point that isn't on the line into the inequality as a test\r\n" );
document.write( "point.  The easiest test point to substitute is the origin (0,0).  We can use\r\n" );
document.write( "it as a test point because (0,0) doesn't lie on the line.  Substituting\r\n" );
document.write( "(x,y) = (0,0)\r\n" );
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document.write( "x + y ≤ 4\r\n" );
document.write( "0 + 0 ≤ 4\r\n" );
document.write( "    0 ≤ 4   <--- this is true so the solutions lie on the side of the line which\r\n" );
document.write( "the test point (0,0), the origin, lies on, which is BELOW and to the LEFT of the\r\n" );
document.write( "green line.\r\n" );
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document.write( "Next we graph the second boundary line (in blue), 2x - y = 4, which has\r\n" );
document.write( "intercepts (0,-4) and (2,0)\r\n" );
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document.write( "Let's find out which side of the line all the solutions to the inequality\r\n" );
document.write( "2x - y ≤ 4 are on.  Again we do that by substituting any point that isn't on the\r\n" );
document.write( "line into the inequality as a test point.  The easiest test point to substitute,\r\n" );
document.write( "again,  is the origin (0,0).  We can use it again as a test point because (0,0)\r\n" );
document.write( "doesn't lie on the line.  Substituting\r\n" );
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document.write( "(x,y) = (0,0)\r\n" );
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document.write( "  2x - y ≤ 4\r\n" );
document.write( "2(0) + 0 ≤ 4\r\n" );
document.write( "       0 ≤ 4   <--- this is true so the solutions lie on the side of the line which\r\n" );
document.write( "the test point (0,0), the origin, lies on, which is ABOVE and to the LEFT of the\r\n" );
document.write( "blue line.\r\n" );
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document.write( "So finally we shade the area which is BELOW and to the LEFT of the\r\n" );
document.write( "green line AND which is ABOVE and to the LEFT of the blue line.\r\n" );
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document.write( "Edwin
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