Question

Is (–10, 8) a solution to this system of inequalities?

y< 1/10x+ 9
y≥ –1/5x+ 5

Answer 1

To determine if the point \((-10, 8)\) is a solution to the system of inequalities, we need to substitute \(x = -10\) and \(y = 8\) into each inequality and check if they hold true.

1. **First Inequality:**
\[
y < \frac{1}{10}x + 9
\]
Substitute \(x = -10\) and \(y = 8\):
\[
8 < \frac{1}{10}(-10) + 9
\]
Simplifying the right side:
\[
8 < -1 + 9
\]
\[
8 < 8
\]
This is **not true**.

2. **Second Inequality:**
\[
y \geq -\frac{1}{5}x + 5
\]
Substitute \(x = -10\) and \(y = 8\):
\[
8 \geq -\frac{1}{5}(-10) + 5
\]
Simplifying the right side:
\[
8 \geq 2 + 5
\]
\[
8 \geq 7
\]
This is **true**.

Since the first inequality is not satisfied, the point \((-10, 8)\) is **not** a solution to the system of inequalities.