JAMB 2000 · UME · Q17✱✱

Which of the graphs represents the solution of the simultaneous inequalities $2x - 2 \le y$ and $2y - 2 \le x$ ?

Worked solution (try it first)

$2x - 2 \le y$ is the region on or above the line $y = 2x - 2$ , through $(1, 0)$ and $(0, -2)$ .
Rearrange $2y - 2 \le x$ : add 2 and divide by 2 to get $y \le \frac12x + 1$ , the region on or below the line through $(-2, 0)$ and $(0, 1)$ .
The lines meet at $(2, 2)$ .
Test the origin: $-2 \le 0$ and $-2 \le 0$ are both true, so the region contains $(0, 0)$ .
Graph B shades the wedge between these two lines that contains the origin, so the answer is option B.