Question

Is (–2, –3) a solution to this system of inequalities?

20x − 11y ≤ –11
2x − 12y > –14

Answer 1

To check if \((-2, -3)\) is a solution to the system of inequalities, we need to substitute \(x = -2\) and \(y = -3\) into each inequality and see if they hold true.

1. **First Inequality: \(20x - 11y \leq -11\)**

Substituting \(x = -2\) and \(y = -3\):

\[
20(-2) - 11(-3) \leq -11
\]

\[
-40 + 33 \leq -11
\]

\[
-7 \leq -11
\]

This is **false**.

2. **Second Inequality: \(2x - 12y > -14\)**

Substituting \(x = -2\) and \(y = -3\):

\[
2(-2) - 12(-3) > -14
\]

\[
-4 + 36 > -14
\]

\[
32 > -14
\]

This is **true**.

Since \((-2, -3)\) does not satisfy the first inequality but satisfies the second inequality, it is **not a solution** to the system of inequalities.