Question

Is (–5, 10) a solution to this system of inequalities?

15x + 4y ≥ 15
y > 9

Answer 1

To determine if the point \((-5, 10)\) is a solution to the system of inequalities, we need to substitute \(x = -5\) and \(y = 10\) into each inequality and check if they hold true.

1. **First inequality:** \(15x + 4y \geq 15\)

Substituting \(x = -5\) and \(y = 10\):

\[
15(-5) + 4(10) \geq 15
\]
\[
-75 + 40 \geq 15
\]
\[
-35 \geq 15 \quad (\text{This is false})
\]

2. **Second inequality:** \(y > 9\)

Substituting \(y = 10\):

\[
10 > 9 \quad (\text{This is true})
\]

The first inequality is false, so the point \((-5, 10)\) does not satisfy the entire system of inequalities. Therefore, \((-5, 10)\) is **not** a solution to the system.