Question

Which system of linear inequalities is represented by the graph?

y > x – 2 and x – 2y < 4
y > x + 2 and x + 2y < 4
y > x – 2 and x + 2y < 4
y > x – 2 and x + 2y < –4

Answer 1

I don’t see the graph — could you upload it or describe which region is shaded and whether the boundary lines are dashed or solid?

Meanwhile, here is a quick way you can identify the correct system from the graph:

1. Rewrite each inequality as y = ... (the boundary line) and note its slope and y-intercept:
- y > x – 2 (boundary y = x − 2, slope 1, y-intercept −2)
- y > x + 2 (boundary y = x + 2, slope 1, y-intercept 2)
- x − 2y < 4 ⇔ y > 0.5x − 2 (boundary y = 0.5x − 2, slope 0.5, y-int −2)
- x + 2y < 4 ⇔ y < −0.5x + 2 (boundary y = −0.5x + 2, slope −0.5, y-int 2)
- x + 2y < −4 ⇔ y < −0.5x − 2 (boundary y = −0.5x − 2, y-int −2)

2. Note dashed vs solid: dashed means strict (>, <), solid means ≥ or ≤.

3. Test a convenient point (like (0,0) or (3,3)) that is clearly inside the shaded region on the graph:
- If (0,0) is shaded, options A and C both include the origin; B and D do not.
- To distinguish A vs C: test (3,3). For A (y > x−2 and x−2y < 4) (3,3) satisfies both, so (3,3) would be in A. For C (y > x−2 and x+2y < 4) (3,3) fails x+2y < 4, so (3,3) would not be in C.

Tell me which region is shaded (or upload the graph) and I’ll pick the correct option.