Question

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

y> - 2x+2
y < 2x + 3.

A.(2,2),(3,1),(4,2)
B.(2,2),(3,−1),(4,1)
C.(2,2),(1,−2),(0,2)
D. None of the above

Answer 1

Upon testing, the ordered pairs (2, 2) and (4, 1) satisfy both inequalities y > -2x + 2 and y < 2x + 3.

The correct answer with the solution set of the system of linear inequalities is option B). (2, 2), (3, -1), (4, 1).

Step-by-step explanation:

To determine which ordered pairs are in the solution set of the system of linear inequalities y > -2x + 2 and y < 2x + 3, we need to test each ordered pair to see if it satisfies both inequalities.

(2, 2): For y = 2, does 2 > -2(2) + 2? Yes, because 2 > -2 + 2 = 2.

Does 2 < 2(2) + 3? Yes, because 2 < 4 + 3 = 7. This pair satisfies both inequalities.

(3, 1): For y = 1, does 1 > -2(3) + 2? No, because 1 is not greater than -6 + 2 = -4.

This pair does not satisfy the first inequality.

(4, 2): For y = 2, does 2 > -2(4) + 2? No, because 2 is not greater than -8 + 2 = -6.

This pair does not satisfy the first inequality.

(3, -1): For y = -1, does -1 > -2(3) + 2? No, because -1 is not greater than -6 + 2 = -4.

This pair does not satisfy the first inequality.

(4, 1): For y = 1, does 1 > -2(4) + 2? Yes, because 1 > -8 + 2 = -6. Does 1 < 2(4) + 3? Yes, because 1 < 8 + 3 = 11.

This pair satisfies both inequalities.

Based on the testing above, the ordered pairs in the solution set are (2, 2) and (4, 1).

Therefore, the correct answer is B). (2, 2), (3, −1), (4, 1).