Question

A graphed system of linear inequalities is shown below.
A dashed line passes through the points (-2, 0) and (0, 1) and a solid line passes through the points (0, -3), (2, -7). The area to the right of the intersecting point and between the lines is shaded

Which of the following ordered pairs is a solution to the system of inequalities? Select all that apply.

Answer 1

I need the list of answer choices to pick from. Meanwhile here's how to tell which points are solutions:

- Dashed line through (-2,0) and (0,1): y = (1/2)x + 1 (dashed → strict inequality).
- Solid line through (0,-3) and (2,-7): y = -2x - 3 (solid → nonstrict inequality).
- Intersection: solve (1/2)x + 1 = -2x - 3 → x = -8/5 (−1.6), y = 1/5 (0.2).

The shaded region is to the right of the intersection and between the lines, so the solution set is
x > −8/5 and −2x − 3 ≤ y < (1/2)x + 1.

Give me the ordered pairs to test and I will mark which satisfy these inequalities. (Quick examples: (0,0) is a solution; (-2,0) is not because it lies on the dashed line; (2,-7) is a solution because it lies on the solid line and is between the lines.)