document.write( "Question 75653: solve by graphing linear inequalities
\n" ); document.write( "3x-y<2
\n" ); document.write( "x+y>2
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Algebra.Com's Answer #54340 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"3x-y%3C2\" solve for y
\n" ); document.write( "\"-y%3C2-3x\" Subtract 3x from both sides
\n" ); document.write( "\"y%3E3x-2\" Divide both sides by -1. When dividing by a negative, flip the inequality
\n" ); document.write( "Solve the 2nd equation for y:
\n" ); document.write( "\"x%2By%3E2\"
\n" ); document.write( "\"y%3E2-x\" Subtract x from both sides
\n" ); document.write( "So we can now graph \"y%3E2-x\" and \"y%3E3x-2\". We just graph the equations as we normally would if they were \"y=3x-2\" and \"y=2-x\". Here's the graph:\r
\n" ); document.write( "\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+3x-2%2C2-x%29+\"\r
\n" ); document.write( "\n" ); document.write( "Now lets pick the test point (0,0) to see which region we should shade:
\n" ); document.write( "\"0%3E2-0\"
\n" ); document.write( "\"0%3E2\" false. so we don't shade the region containing (0,0) for that inequality. This means we shade above the line \"y=2-x\" (green line). Now lets test it on the 2nd inequality:
\n" ); document.write( "\"0%3E3%280%29-2\"
\n" ); document.write( "\"0%3E-2\" true. So we shade the region containing (0,0) for the inequality \"y%3E3x-2\" (the upper side of the red line). These regions intersect in the top most region above both of the lines. This is where the solution set lies.
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