Question

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

7x + 20y < –13
18x − 7y > –10

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 check if they hold true.

1. **First inequality:**
\[
7x + 20y < -13
\]
Substitute \( x = 3 \) and \( y = -9 \):
\[
7(3) + 20(-9) < -13
\]
\[
21 - 180 < -13
\]
\[
-159 < -13
\]
This inequality is **true**.

2. **Second inequality:**
\[
18x - 7y > -10
\]
Substitute \( x = 3 \) and \( y = -9 \):
\[
18(3) - 7(-9) > -10
\]
\[
54 + 63 > -10
\]
\[
117 > -10
\]
This inequality is also **true**.

Since both inequalities are satisfied by the point (3, -9), we conclude that (3, -9) is indeed a solution to the system of inequalities.