Question

Which system of linear inequalities is represented by the graph?

y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x +

Answer 1

I can’t see the graph you mean — could you upload it or describe it (where the shading is, whether the boundary lines are dashed or solid, and their intercepts)?

Meanwhile, here is how you can decide which system is shown:

1. Identify the two boundary lines. They look like y = x − 2 (slope 1, y‑intercept −2) and y = x + 1 (slope 1, y‑intercept 1).
2. Check whether each boundary is dashed (strict inequality, > or <) or solid (≥ or ≤).
3. Determine which side of each line is shaded. A quick way: pick a test point not on the line (often (0,0) if it’s not on the line):
- For y = x − 2, plug (0,0): 0 ? (0 − 2) → 0 ? −2. If the shaded region contains (0,0), then the correct relation for that line is 0 > −2 (so y > x − 2). If (0,0) is not shaded then the region is y < x − 2.
- For y = x + 1, plug (0,0): 0 ? (0 + 1) → 0 ? 1. If (0,0) is shaded then the relation is 0 < 1 (so y < x + 1). If not shaded then y > x + 1.
4. Combine the two results.

Example: if the region between the two parallel dashed lines is shaded and it includes the origin, then the system is
y > x − 2 and y < x + 1.

If you upload the graph or describe where the shading lies, I’ll pick the correct option for you.