SOLUTION: solve by graphing linear inequalities 3x-y<2 x+y>2

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Question 75653: solve by graphing linear inequalities
3x-y<2
x+y>2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x-y%3C2 solve for y
-y%3C2-3x Subtract 3x from both sides
y%3E3x-2 Divide both sides by -1. When dividing by a negative, flip the inequality
Solve the 2nd equation for y:
x%2By%3E2
y%3E2-x Subtract x from both sides
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:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+3x-2%2C2-x%29+
Now lets pick the test point (0,0) to see which region we should shade:
0%3E2-0
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:
0%3E3%280%29-2
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.