Question

what point is a solution to the linear inequality 4x - y ≤ 10

(3, 0)
(3.5, -1)
(5, 0)
(2, -2)

Answer 1

To determine which points are solutions to the linear inequality \( 4x - y \leq 10 \), we will substitute the coordinates of each point into the inequality and check if it holds true.

1. For the point \( (3, 0) \):
\[
4(3) - 0 \leq 10 \\
12 \leq 10 \quad \text{(False)}
\]

2. For the point \( (3.5, -1) \):
\[
4(3.5) - (-1) \leq 10 \\
14 + 1 \leq 10 \\
15 \leq 10 \quad \text{(False)}
\]

3. For the point \( (5, 0) \):
\[
4(5) - 0 \leq 10 \\
20 \leq 10 \quad \text{(False)}
\]

4. For the point \( (2, -2) \):
\[
4(2) - (-2) \leq 10 \\
8 + 2 \leq 10 \\
10 \leq 10 \quad \text{(True)}
\]

The only point that satisfies the inequality \( 4x - y \leq 10 \) is \( (2, -2) \).