Question

Which point is in the solution set of the given system of inequalities?
x+y greater than 2
4xy greater than or equal to 2

(2, 0)
(0, 2)
(0, 3)
(0, –1)

Answer 1

None of them.

Check each:
- (2,0): x+y = 2 (not > 2).
- (0,2): x+y = 2 (not > 2).
- (0,3): x+y = 3 (>2) but 4xy = 0 (<2).
- (0,−1): x+y = −1 (not > 2).

So no listed point satisfies both x + y > 2 and 4xy ≥ 2.