Is (1, 10) a solution to this system of inequalities?



*y* ≥ 8*x* + 2
*y* ≥ *x* + 10

To determine if \((1, 10)\) is a solution to the system of inequalities, we need to substitute \( x = 1 \) and \( y = 10 \) into each inequality and check if they hold true.

### Step 1: Substitute \((1, 10)\) into each inequality

1. **First inequality:** \( y \geq 8x + 2 \)
   - Substitute \( x = 1 \) and \( y = 10 \):
   \[
   10 \geq 8(1) + 2
   \]
   - Simplify the right side:
   \[
   10 \geq 8 + 2
   \]
   \[
   10 \geq 10
   \]
   This inequality holds because \( 10 = 10 \).

2. **Second inequality:** \( y \geq x + 10 \)
   - Substitute \( x = 1 \) and \( y = 10 \):
   \[
   10 \geq 1 + 10
   \]
   - Simplify the right side:
   \[
   10 \geq 11
   \]
   This inequality does not hold because \( 10 < 11 \).

### Conclusion
Since the point \((1, 10)\) does not satisfy the second inequality, it is **not** a solution to the system of inequalities.

Would you like further explanation on solving systems of inequalities?

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1. How can I determine if a point lies in the solution set of multiple inequalities?
2. What strategies can I use to graph inequalities on a coordinate plane?
3. How do I check solutions for inequalities with strict inequalities (e.g., \(>\) or \(<\))?
4. Can a point be a solution for one inequality but not the entire system?
5. What is the difference between systems of inequalities and systems of equations?

**Tip:** Always test each inequality separately when working with systems of inequalities.

Is (1, 10) a solution to this system of inequalities?

y ≥ 8x + 2
y ≥ x + 10

Explore how to determine if the point (1, 10) satisfies the system of inequalities y ≥ 8x + 2 and y ≥ x + 10. This step-by-step guide is suitable for students in Grades 9-11 and includes substitution methods and solution verification.

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