Question

consider the system of inequalities and its graph.
y ≤ -0.75x
y ≤ 3x - 2
in which section of the graph does the actual solution to the system lie?
○ 1
○ 2
○ 3
○ 4

Explanation:

Step1: Analyze \( y \leq -0.75x \)

The inequality \( y \leq -0.75x \) represents the region below (or on) the line \( y = -0.75x \). From the graph, this line has a negative slope, passing through the origin. The regions below this line are sections 1, 4 (since the line divides the plane, and below is towards lower \( y \)-values relative to the line).

Step2: Analyze \( y \leq 3x - 2 \)

The inequality \( y \leq 3x - 2 \) represents the region below (or on) the line \( y = 3x - 2 \). This line has a positive slope, with a \( y \)-intercept at \( -2 \). The regions below this line are sections 3, 4 (as the line's lower side is towards lower \( y \)-values relative to the line).

Step3: Find Intersection of Regions

The solution to the system is the intersection of the regions defined by both inequalities. The intersection of the regions (below \( y = -0.75x \) and below \( y = 3x - 2 \)) is section 4, as it is the area that satisfies both "below" conditions for each line.

Answer:

4