Question

x - 4y ≤ 4
y < x + 1

Explanation:

Step1: Rewrite first inequality

Rearrange $x-4y\leq4$ to slope-intercept form:

$$\begin{align*} -4y&\leq -x + 4\\ y&\geq \frac{1}{4}x - 1 \end{align*}$$

This means we shade above the solid line $y=\frac{1}{4}x - 1$.

Step2: Analyze second inequality

The inequality $ybelow the dashed line $y=x+1$.

Step3: Identify overlapping region

The solution is the area that is shaded for both inequalities: above the solid line $y=\frac{1}{4}x - 1$ and below the dashed line $y=x+1$. This matches the third graph (top right).

Answer:

The correct graph is the third one (top right, the graph with overlapping blue and red shading covering the upper left and lower right regions relative to the lines).