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)

Answer 1

Check each point in y > -1/3 x + 2 and y < 2x + 3.

(2,2): -1/3(2)+2 = 4/3, 2 > 4/3 (true); 2 < 7 (true). → in solution.
(3,1): -1/3(3)+2 = 1, 1 > 1 (false). → not in solution.
(4,2): -1/3(4)+2 = 2 - 4/3 = 2/3, 2 > 2/3 (true); 2 < 11 (true). → in solution.
(3,−1): -1/3(3)+2 = 1, −1 > 1 (false). → not in solution.
(4,1): -1/3(4)+2 = 2/3, 1 > 2/3 (true); 1 < 11 (true). → in solution.

So the points from the lists that satisfy both inequalities are (2,2), (4,2), and (4,1). Neither given three-point choice is entirely correct.