Question

Is (–3, –9) a solution to this system of inequalities?

y ≤ 6x + 9
y ≤ 5x + 6

Answer 1

To determine if the point \((-3, -9)\) is a solution to the system of inequalities, we will substitute \(x = -3\) and \(y = -9\) into each inequality and see if the inequalities hold true.

1. For the first inequality:

\[
y \leq 6x + 9
\]
Substitute \(x = -3\) and \(y = -9\):
\[
-9 \leq 6(-3) + 9
\]
Calculate the right side:
\[
6(-3) + 9 = -18 + 9 = -9
\]
Therefore, we have:
\[
-9 \leq -9
\]
This inequality is true.

2. For the second inequality:

\[
y \leq 5x + 6
\]
Substitute \(x = -3\) and \(y = -9\):
\[
-9 \leq 5(-3) + 6
\]
Calculate the right side:
\[
5(-3) + 6 = -15 + 6 = -9
\]
Therefore, we have:
\[
-9 \leq -9
\]
This inequality is also true.

Since \((-3, -9)\) satisfies both inequalities, it is indeed a solution to the system of inequalities.