The question asks whether the point $(x = 2, y = -1)$ is a solution to a series of inequalities.

Let's evaluate each inequality by substituting $x = 2$ and $y = -1$ into them:

1. $-6x - 9y < -3$

Substitute $x = 2$ and $y = -1$ into the inequality: $-6(2) - 9(-1) = -12 + 9 = -3$ This results in $-3 < -3$, which is false. So, $(x = 2, y = -1)$ is not a solution for this inequality.

2. $-6x - 9y \leq -3$

Substitute $x = 2$ and $y = -1$: $-6(2) - 9(-1) = -12 + 9 = -3$ This results in $-3 \leq -3$, which is true. So, $(x = 2, y = -1)$ is a solution for this inequality.

3. $-6x - 9y > -3$

Substitute $x = 2$ and $y = -1$: $-6(2) - 9(-1) = -12 + 9 = -3$ This results in $-3 > -3$, which is false. So, $(x = 2, y = -1)$ is not a solution for this inequality.

4. $-6x - 9y \geq -3$

Substitute $x = 2$ and $y = -1$: $-6(2) - 9(-1) = -12 + 9 = -3$ This results in $-3 \geq -3$, which is true. So, $(x = 2, y = -1)$ is a solution for this inequality.

Conclusion:

• For the inequality $-6x - 9y < -3$, the point is not a solution.
• For the inequality $-6x - 9y \leq -3$, the point is a solution.
• For the inequality $-6x - 9y > -3$, the point is not a solution.
• For the inequality $-6x - 9y \geq -3$, the point is a solution.

Would you like more details on any of these steps or explanations?

Here are 5 related questions you can explore:

1. How do you solve linear inequalities with two variables?
2. What does it mean for a point to be a solution to an inequality?
3. How do you graph the inequality $-6x - 9y \leq -3$?
4. What are some methods to check if a point satisfies a system of inequalities?
5. What is the difference between strict inequalities and non-strict inequalities?

Tip: When testing points in inequalities, always substitute the values carefully and ensure you check the inequality sign, especially for "strict" (e.g., <) and "non-strict" (e.g., ≤) cases.