Which of the following points is a solution to the linear inequality 4x−y≤10, as shown on the graph?

Option #1: (2 1/2,−1/2)
Option #2: (2,−3)
Option #3: (3,2)

1 answer

To determine which of the given points is a solution to the linear inequality \( 4x - y \leq 10 \), we can substitute each point into the inequality.

Option #1: \( (2.5, -0.5) \)
Substituting \( x = 2.5 \) and \( y = -0.5 \): \[ 4(2.5) - (-0.5) \leq 10 \ 10 + 0.5 \leq 10 \ 10.5 \leq 10 \quad \text{(False)} \]

Option #2: \( (2, -3) \)
Substituting \( x = 2 \) and \( y = -3 \): \[ 4(2) - (-3) \leq 10 \ 8 + 3 \leq 10 \ 11 \leq 10 \quad \text{(False)} \]

Option #3: \( (3, 2) \)
Substituting \( x = 3 \) and \( y = 2 \): \[ 4(3) - 2 \leq 10 \ 12 - 2 \leq 10 \ 10 \leq 10 \quad \text{(True)} \]

The only point that satisfies the inequality \( 4x - y \leq 10 \) is Option #3: \( (3, 2) \).