Question

question 4 of 10
on a piece of paper, graph this system of inequalities. then determine which
region contains the solution to the system.

y ≤ (1/4)x + 3
y ≥ -x + 5

graph with regions a, b, c, d
text description for graph

a. region c
b. region a
c. region b
d. region d

Explanation:

Step 1: Analyze \( y \leq \frac{1}{4}x + 3 \)

The line \( y=\frac{1}{4}x + 3 \) has a slope of \( \frac{1}{4} \) and y - intercept at \( (0,3) \). The inequality \( y \leq \frac{1}{4}x + 3 \) means we shade below this line (including the line itself).

Step 2: Analyze \( y \geq -x + 5 \)

The line \( y=-x + 5 \) has a slope of \( - 1 \) and y - intercept at \( (0,5) \). The inequality \( y \geq -x + 5 \) means we shade above this line (including the line itself).

Step 3: Find the intersection region

To find the solution of the system, we need the region that is shaded both below \( y=\frac{1}{4}x + 3 \) and above \( y=-x + 5 \). By looking at the graph, Region C is the region that satisfies both inequalities.

Answer:

A. Region C