Question

which graph shows the solution to the system of linear inequalities?
x - 4y ≤ 4
y < x + 1

Explanation:

Step1: Analyze \( x - 4y \leq 4 \)

Rewrite it as \( y \geq \frac{x - 4}{4}=\frac{1}{4}x - 1 \). The boundary line \( y=\frac{1}{4}x - 1 \) is solid (since \( \leq \)), and we shade above the line (because \( y\geq \)).

Step2: Analyze \( y < x + 1 \)

The boundary line \( y = x + 1 \) is dashed (since \( < \)), and we shade below the line (because \( y< \)).

Step3: Match with graphs

• Check the boundary lines: \( y=\frac{1}{4}x - 1 \) (solid) and \( y = x + 1 \) (dashed).
• Check shading: Above \( y=\frac{1}{4}x - 1 \) and below \( y = x + 1 \). The second graph (top - right) has a dashed line for \( y=x + 1 \), solid for \( y=\frac{1}{4}x - 1 \), and correct shading.

Answer:

The top - right graph (the second graph in the top row)