Question

How do you graph the system `y< 3/2x -2` and `2y > x -4`?

Answer 1

(1) y - (3x)/2 + 2 < 0

(2) 2y - x + 2 > 0

First, graph the Line `y1 = = (3x)/2 - 2`
Use the origin as test point: x = 0 -> 2 < 0. Not true. Then the origin doesn't belong to the solution set. The solution set of the inequality (1) is the area below the line. Color this area.
Next, graph the Line `y2 = x/2 - 2.`
Use O as test point: x = 0 -> +2 > 0. True. Then, O belongs to the solution set. The solution set of the inequality (2) is the area above this line. Color it.
The combined solution set of the system is the commonly shared area.