document.write( "Question 1010660: 2x-y (less than or equal to) 4
\n" ); document.write( "x+2y (greater than or equal to) 6\r
\n" ); document.write( "\n" ); document.write( "I need to solve both these inequalities to find the correct solution set out of two possible sets. Thanks. \n" ); document.write( "
Algebra.Com's Answer #626475 by KMST(5328)\"\" \"About 
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\"2x-y%3C=4\" includes the line with equation \"2x-y=4\" and half of the x-y plane to one side of that line.
\n" ); document.write( "To graph that lien we only need to points.
\n" ); document.write( "\"system%28x=0%2C2x-y=4%29\"-->\"system%28x=0%2C-y=4%29\"-->\"system%28x=0%2Cy=-4%29\" ,
\n" ); document.write( "so point (0,-4) belongs to the line with equation \"2x-y=4\" .
\n" ); document.write( "\"system%28y=0%2C2x-y=4%29\"-->\"system%28y=0%2C2x=4%29\"-->\"system%28y=0%2Cx=2%29\" ,
\n" ); document.write( "so point (2,0) belongs to the line with equation \"2x-y=4\" .
\n" ); document.write( "With those two points we can graph line \"2x-y=4\" as
\n" ); document.write( "\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C2x-4%29\" .
\n" ); document.write( "Since point (0,0) , the origin, satisfies \"2x-y%3C=4\" ,
\n" ); document.write( "because \"2%2A0-0=0%3C4\" ,
\n" ); document.write( "the half of the x-y plane that is the graph of \"2x-y%3C=4\" is
\n" ); document.write( "\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C2x-y%3C=4%29\" , the half of the x-y plane that contains the origin.
\n" ); document.write( "We can do the same for \"x%2B2y%3E=6\" :
\n" ); document.write( "\"system%28x=0%2Cx%2B2y=6%29\"-->\"system%28x=0%2C2y=6%29\"-->\"system%28x=0%2Cy=3%29\" ,
\n" ); document.write( "so point (0,3) belongs to the line with equation \"x%2B2y=6\" .
\n" ); document.write( "\"system%28y=0%2Cx%2B2y=6%29\"-->\"system%28y=0%2Cx=6%29\"- ,
\n" ); document.write( "so point (6,0) belongs to the line with equation \"x%2B2y=6\" .
\n" ); document.write( "With those two points we can graph line \"x%2B2y=6\" as
\n" ); document.write( "\"graph%28300%2C300%2C-2%2C8%2C-5%2C5%2C-0.5x%2B3%29\" .
\n" ); document.write( "Since point (0,0) , the origin, does not satisfy \"x%2B2y%3E=6\" ,
\n" ); document.write( "because \"0%2B2%2A0=0%3C6\" ,
\n" ); document.write( "the half of the x-y plane that is the graph of \"2x-y%3C=4\" is
\n" ); document.write( "\"graph%28300%2C300%2C-2%2C8%2C-5%2C5%2Cx%2B2y%3E=6%29\" , the half of the x-y plane that does not contain the origin.
\n" ); document.write( "So the solution to \"system%282x-y%3C=4%2Cx%2B2y%3E=6%29\" is graphed as the shaded area below.
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