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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.

Is x = 2 and y = -1 a solution of the following inequalities?

1. -6x - 9y < -3
2. -6x - 9y ≤ -3
3. -6x - 9y > -3
4. -6x - 9y ≥ -3

Check if the point (2, -1) satisfies a series of linear inequalities, including -6x - 9y < -3 and others. This solution involves substitution and solving inequalities, ideal for students in Grades 8-10.

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