Question

Is (4, 2) a solution to this system of inequalities?

3x + y < 15
2x + 2y < 16

Answer 1

To determine whether \((4, 2)\) is a solution to the given system of inequalities, we will substitute \(x = 4\) and \(y = 2\) into both inequalities and check if they hold true.

1. First inequality:
\[
3x + y < 15
\]
Substituting \(x = 4\) and \(y = 2\):
\[
3(4) + 2 < 15
\]
\[
12 + 2 < 15
\]
\[
14 < 15 \quad \text{(True)}
\]

2. Second inequality:
\[
2x + 2y < 16
\]
Substituting \(x = 4\) and \(y = 2\):
\[
2(4) + 2(2) < 16
\]
\[
8 + 4 < 16
\]
\[
12 < 16 \quad \text{(True)}
\]

Since both inequalities are satisfied, \((4, 2)\) is indeed a solution to the system of inequalities.