Substitute the given point (3, -2) in each condition (i) y < -3; y ≤ (2/3)x - 4 -2 < -3 → False Therefore, it is not a solution. [Since the values of x and y must satisfy both the conditions, if one of them does not satisfy the condition then it is not necessary to check the other one.] (ii) y > -3; y ≥ 2/3x - 4 -2 > -3 → True y ≥ 2/3x - 4 -2 ≥ -2 → True Therefore, it is a solution. (iii) y < -3; y ≥ 2/3x - 4 -2 < -3 → False Therefore, it is not a solution. (iv) y > -2; y ≤ 2/3x - 4 -2 > -2 → False Therefore, it is not a solution. Thereofore, the system of linear inequalities having the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4. Hope it helps you.
