Which point satisfies the system x + 2y ≤ 10, 2x − y ≥ 3, x ≥ 0, y ≥ 0?

Correct answer: (3, 2)

A point is a solution only if it satisfies every inequality at the same time. Test option B, (3, 2): x + 2y = 3 + 2(2) = 7 ≤ 10, and 2x − y = 2(3) − 2 = 4 ≥ 3. Both coordinates are non-negative, so all four conditions hold. The distractors fail as follows: (1, 4) gives 2x − y = −2, which is too small; (0, 5) gives −5, also too small; and (2, 5) gives x + 2y = 12, which exceeds 10. Thus (3, 2) is the only feasible point, so option B is correct. Direct substitution is sufficient and avoids any ambiguity from a sketch.