Question

Is (5, 2) a solution to this system of inequalities?

16x + 14y > 11
19x + y ≤ 3

Answer 1

To determine if the point \((5, 2)\) is a solution to the given system of inequalities, we need to substitute \(x = 5\) and \(y = 2\) into each inequality and check whether the resulting statements are true.

1. **For the first inequality:**
\[
16x + 14y > 11
\]
Substitute \(x = 5\) and \(y = 2\):
\[
16(5) + 14(2) > 11
\]
This simplifies to:
\[
80 + 28 > 11
\]
\[
108 > 11
\]
This statement is **true**.

2. **For the second inequality:**
\[
19x + y \leq 3
\]
Substitute \(x = 5\) and \(y = 2\):
\[
19(5) + 2 \leq 3
\]
This simplifies to:
\[
95 + 2 \leq 3
\]
\[
97 \leq 3
\]
This statement is **false**.

Since the point \((5, 2)\) satisfies the first inequality but does not satisfy the second inequality, it is **not a solution** to the system of inequalities.