Question

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

y ≥ x + 3
y < 4x + 2

Answer 1

To determine if the point (2, 5) is a solution to the system of inequalities, we need to check whether the coordinates \(x = 2\) and \(y = 5\) satisfy both inequalities.

1. **First inequality**: \(y \geq x + 3\)
\[
5 \geq 2 + 3
\]
\[
5 \geq 5 \quad \text{(true)}
\]
So, (2, 5) satisfies the first inequality.

2. **Second inequality**: \(y < 4x + 2\)
\[
5 < 4(2) + 2
\]
\[
5 < 8 + 2
\]
\[
5 < 10 \quad \text{(true)}
\]
So, (2, 5) also satisfies the second inequality.

Since the point (2, 5) satisfies both inequalities, we conclude that it is indeed a solution to the system of inequalities.