Question

Which number completes the system of linear inequalities represented by the graph?

y > 2x – 2 and x + 4y >

Answer 1

I don’t have the graph image, so I can’t read the missing number directly. Can you either upload the graph or tell me coordinates of two points on the boundary line (or the x‑ and y‑intercepts) and which side is shaded?

How you (or I) would find the number from the graph:
1. Identify two clear points on the boundary line (for example the x‑ and y‑intercepts).
2. Plug one of those points into x + 4y = ? to compute the constant on the right hand side. That gives the full equation x + 4y = c for the boundary.
3. Look at whether the boundary is dashed (strict > or <) or solid (≥ or ≤) to choose > or <.
4. To determine whether it’s > or <, test any point from the shaded region (for example (0,0) if it’s not on the line): if x+4y at that point is greater than c then the inequality is x+4y > c; otherwise x+4y < c.

Example: if the boundary passes through (0,2) and (4,0) then plugging (0,2) gives 0+4·2 = 8, so the inequality would be x + 4y > 8 (or < 8 depending on which side is shaded).

Send the graph or two boundary points and I’ll compute the exact number.