Question

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

7x − 9y < 7
2x + 12y > –2

Answer 1

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

1. For the first inequality:
\( 7x - 9y < 7 \)

Substitute \( x = 10 \) and \( y = 10 \):
\[
7(10) - 9(10) < 7
\]
\[
70 - 90 < 7
\]
\[
-20 < 7 \quad \text{(True)}
\]

2. For the second inequality:
\( 2x + 12y > -2 \)

Substitute \( x = 10 \) and \( y = 10 \):
\[
2(10) + 12(10) > -2
\]
\[
20 + 120 > -2
\]
\[
140 > -2 \quad \text{(True)}
\]

Since both inequalities are satisfied, (10, 10) is indeed a solution to the system of inequalities.