To determine if the point (-2, 10) is a solution to the system of inequalities:

1. First inequality: $y > -\frac{1}{2}x + 5$

Substitute $x = -2$ and $y = 10$: $y > -\frac{1}{2}(-2) + 5$ $10 > 1 + 5$ $10 > 6 \quad \text{(True)}$

2. Second inequality: $y < -9$

Substitute $y = 10$: $10 < -9 \quad \text{(False)}$

Since the point (-2, 10) satisfies the first inequality but not the second, the answer is no, (-2, 10) is not a solution to the system of inequalities.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to explore:

1. What is the general method to solve systems of inequalities?
2. How can you graph systems of inequalities?
3. What are boundary lines in inequalities?
4. How does one find if a point is a solution to a single inequality?
5. What changes when inequalities involve $\geq$ or $\leq$?

Tip: Always check both inequalities independently when working with systems!