Question

Which of the following points is a solution to the linear inequality 4x - y ≤ 10
A. (3, 0)
B. (5, 0)
C. (3.5, 1)
D. (2, -2)

Answer 1

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

1. **Point A: (3, 0)**
\[
4(3) - 0 \leq 10 \\
12 \leq 10 \quad \text{(False)}
\]

2. **Point B: (5, 0)**
\[
4(5) - 0 \leq 10 \\
20 \leq 10 \quad \text{(False)}
\]

3. **Point C: (3.5, 1)**
\[
4(3.5) - 1 \leq 10 \\
14 - 1 \leq 10 \\
13 \leq 10 \quad \text{(False)}
\]

4. **Point D: (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 **Point D: (2, -2)**.