Which inequality has a solution of (0, -2)?*3x - 2y ≤ -43x – 2y ≤ 42x – 3y ≤ -42x – 3y ≤ 4

To determine which inequality has a solution of $(0, -2)$, we need to substitute the point $(0, -2)$ into each of the given inequalities.

1. Substitute the Point into Each Inequality

We will evaluate each inequality with $x = 0$ and $y = -2$.

1. For Inequality 1: $3x - 2y \leq -4$ $3(0) - 2(-2) \leq -4 \implies 0 + 4 \leq -4 \implies 4 \leq -4 \quad \text{(False)}$

2. For Inequality 2: $3x - 2y \leq 4$ $3(0) - 2(-2) \leq 4 \implies 0 + 4 \leq 4 \implies 4 \leq 4 \quad \text{(True)}$

3. For Inequality 3: $2x - 3y \leq -4$ $2(0) - 3(-2) \leq -4 \implies 0 + 6 \leq -4 \implies 6 \leq -4 \quad \text{(False)}$

4. For Inequality 4: $2x - 3y \leq 4$ $2(0) - 3(-2) \leq 4 \implies 0 + 6 \leq 4 \implies 6 \leq 4 \quad \text{(False)}$

2. Identify True Inequality

From our evaluation, we see that only Inequality 2 is true when substituting the point $(0, -2)$.

Final Answer

The inequality that has a solution of $(0, -2)$ is: $3x - 2y \leq 4$