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 + 1

Answer 1

I can’t see the graph — could you upload it or describe which region is shaded (for example: the region between the two lines, above both lines, below both lines, or outside between them)?

How to decide from the graph:
- Identify the two boundary lines: y = x − 2 and y = x + 1. If the lines are dashed, the inequalities are strict (>, <); if solid, they are ≥ or ≤.
- Pick any test point in the shaded region (a convenient one is often (0,0) unless it lies on a boundary).
- Substitute the test point into each candidate inequality:
- If the test point makes the inequality true, that inequality matches the shading side of that line.
- If false, the correct inequality for that line is the opposite sign.

Example: if the graph shades the strip between the two dashed lines, the correct system is
y > x − 2 and y < x + 1
(because points between the lines are above y = x − 2 but below y = x + 1). If you send the image or describe which side is shaded, I’ll pick the exact option.