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 (including the line) the line \( y = -0.75x \). This line has a negative slope and passes through the origin.

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

The inequality \( y \leq 3x - 2 \) represents the region below (including the line) the line \( y = 3x - 2 \). This line has a positive slope and a \( y \)-intercept of \( -2 \).

Step3: Find the intersection of regions

The solution to the system of inequalities is the region that satisfies both inequalities. So we need the area that is below both \( y = -0.75x \) and \( y = 3x - 2 \). By looking at the graph, we can see that section 3 is the area that is below both lines.

Answer:

3