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)

1 answer

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).