Question

1. which of the following are a solution to the system of inequalities shown in the graph? a. (3,2) b. (-1,4) c. (-2,0) d. (-4,3) e. (5,5) f. (0,2)

Explanation:

To determine which points are solutions to the system of inequalities, we check if each point lies in the overlapping (feasible) region of the graph.

Analyzing Each Option:

• Option A: (3,2)

Visually, (3,2) does not lie in the overlapping shaded region (the intersection of all shaded areas).

• Option B: (-1,4)

(-1,4) lies in the region where all shaded areas overlap (the purple, blue, and red regions intersect here).

• Option C: (-2,0)

(-2,0) lies in the overlapping region (part of the blue and purple shaded areas).

• Option D: (-4,3)

(-4,3) lies in the overlapping region (part of the blue and purple shaded areas).

• Option E: (5,5)

(5,5) does not lie in the overlapping shaded region.

• Option F: (0,2)

(0,2) does not lie in the overlapping shaded region (it is on the boundary or outside the intersection).

• B (-1,4): Lies in the intersection of all shaded regions.
• C (-2,0): Lies in the overlapping blue and purple regions.
• D (-4,3): Lies in the overlapping blue and purple regions.

Answer:

B. (-1,4), C. (-2,0), D. (-4,3)