Question

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)

Answer 1

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: \( (3, 2) \)**.