Is (-2,10) a solution to this system of inequalites y> -1/2x+5,y<-9 yes or no

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!

Is (-2,10) a solution to this system of inequalities y > -1/2x + 5, y < -9 yes or no

Discover how to determine if the point (-2, 10) is a solution to the system of inequalities y > -1/2x + 5 and y < -9. This problem uses algebraic substitution to check solutions for systems of inequalities and is suitable for students in Grades 7-10.

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