document.write( "Question 117186: Graph y>2x+1 and 2x+y>2 \n" ); document.write( "
Algebra.Com's Answer #86123 by Edwin McCravy(20055)\"\" \"About 
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Graph y > 2x + 1 and 2x + y > 2
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document.write( "First graph only the first boundary line, which is the\r\n" );
document.write( "first inequality with the > replaced by =.  That is the\r\n" );
document.write( "line whose equation is y = 2x + 1\r\n" );
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document.write( "So we draw the graph of the first boundary line by getting \r\n" );
document.write( "a couple of points.  We draw a GREEN dotted line through them, \r\n" );
document.write( "dotted because of the >.  (If it had been > we would \r\n" );
document.write( "have drawn the boundary line solid.)\r\n" );
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document.write( "Before we draw the other boundary line, we must\r\n" );
document.write( "decide which side of the line the final shading\r\n" );
document.write( "must be on.  To do this we choose any point which \r\n" );
document.write( "is not on the line as a test point.  Let's \r\n" );
document.write( "arbitrarily choose (3,3) on the right side of the\r\n" );
document.write( "line as a test point. Substitute x=3, y=3 into the \r\n" );
document.write( "original inequality:\r\n" );
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document.write( "y > 2x+1\r\n" );
document.write( "3 > 2(3)+1\r\n" );
document.write( "3 > 6+1\r\n" );
document.write( "3 > 7\r\n" );
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document.write( "This is FALSE, so we shade the OPPOSITE side of\r\n" );
document.write( "the line from which (3,3) is on, which is\r\n" );
document.write( "the LEFT side of the GREEN line.\r\n" );
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document.write( "Next we graph the second boundary line, which is the\r\n" );
document.write( "second inequality with the > replaced by =. \r\n" );
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document.write( "2x + y = 2\r\n" );
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document.write( "So we draw the graph of the second boundary line by getting \r\n" );
document.write( "a couple of points.  We draw a BLUE dotted line through them,\r\n" );
document.write( "dotted because of the >.  (Again, if it had been > we \r\n" );
document.write( "would have drawn the boundary line solid.)\r\n" );
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document.write( "As before must decide which side of the BLUE line \r\n" );
document.write( "the final shading must be on.  To do this we choose \r\n" );
document.write( "any point which is not on the BLUE line as a test \r\n" );
document.write( "point.  Let's arbitrarily choose (4,2) on the right \r\n" );
document.write( "side of the BLUE line as a test point. Substitute \r\n" );
document.write( "x=4, y=2 into the original inequality:\r\n" );
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document.write( "    2x + y > 2\r\n" );
document.write( "2(4) + (2) > 2\r\n" );
document.write( "     8 + 2 > 2\r\n" );
document.write( "        10 > 2\r\n" );
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document.write( "This is TRUE, so we DO shade the side of\r\n" );
document.write( "the BLUE line which (4,2) lie on, which is\r\n" );
document.write( "the RIGHT side of the BLUE line.\r\n" );
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document.write( "So we must shade the V-shaped wedge which is\r\n" );
document.write( "LEFT of the GREEN line and RIGHT of the BLUE\r\n" );
document.write( "LINE, as indicated below:\r\n" );
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document.write( "Edwin
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