Question

Choose the graph that matches the system of inequalities.
–x + y ≤ –1
x + 2y ≥ 4
A. Two intersecting solid lines graphed on a coordinate plane. The decreasing line crosses the y axis at 2 and passes through the point 2 comma 1. There is shading below this line. The increasing line crosses the y axis at negative 1 and passes through the point 2 comma 1. There is shading above this line.
B. Two intersecting solid lines graphed on a coordinate plane. The decreasing line crosses the y axis at 2 and passes through the point 2 comma 1. There is shading above this line. The increasing line crosses the y axis at negative 1 and passes through the point 2 comma 1. There is shading below this line.
C. Two intersecting dashed lines graphed on a coordinate plane. The decreasing line crosses the y axis at 2 and passes through the point 2 comma 1. There is shading above this line. The increasing line crosses the y axis at negative 1 and passes through the point 2 comma 1. There is shading below this line.
D. Two intersecting dashed lines graphed on a coordinate plane. The decreasing line crosses the y axis at 2 and passes through the point 2 comma 1. There is shading below this line. The increasing line crosses the y axis at negative 1 and passes through the point 2 comma 1. There is shading above this line.

Answer 1

First rewrite each inequality in y = mx + b form:

- −x + y ≤ −1 → y ≤ x − 1.
Line: y = x − 1 (increasing, y‑intercept −1, passes through (2,1)). Shade below (≤).

- x + 2y ≥ 4 → 2y ≥ −x + 4 → y ≥ −(1/2)x + 2.
Line: y = −(1/2)x + 2 (decreasing, y‑intercept 2, passes through (2,1)). Shade above (≥).

Both inequalities include the boundary, so the lines are solid. This matches choice B.