Question

Which ordered pairs are in the solution set of the system of linear inequalities?

y > Negative one-thirdx + 2

y < 2x + 3

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (6, 0. Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (negative 3, negative 3) and (0, 3). Everything above the line is shaded.

(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)

Answer 1

(2, 2), (3, 1), (4, 2)

Reason: The graph shows the first line solid, so use y ≥ −(1/3)x + 2, and the second dashed line gives y < 2x + 3. Check each point:

- (2,2): 2 ≥ −2/3 + 2 = 4/3 (true) and 2 < 7 (true).
- (3,1): 1 ≥ −1 + 2 = 1 (true) and 1 < 9 (true).
- (4,2): 2 ≥ −4/3 + 2 = 2/3 (true) and 2 < 11 (true).

All three satisfy the system, so the first choice is correct.