Question

Which ordered pair is a solution to the system of inequalities? −x + 3y < 12 x + y ≥ 4 A) (0, 0) B) (−6, 1) C) (3, 3) D) (1, 2)

Answer 1

To find the solution to the system of inequalities, we substitute each ordered pair into the inequalities and check if they are satisfied. Only (1, 2) satisfies both inequalities.

Step-by-step explanation:

To find which ordered pair is a solution to the system of inequalities, we need to substitute each option into the two inequalities and check if the inequalities are satisfied. Let's check each option:

A) (0, 0)

Substituting (0, 0) into the first inequality: -0 + 3(0) < 12, which simplifies to 0 < 12. This is true.

Substituting (0, 0) into the second inequality: 0 + 0 ≥ 4, which simplifies to 0 ≥ 4. This is false.

Since the second inequality is not satisfied, (0, 0) is not a solution to the system of inequalities.

Similarly, we can check the other options:

B) (−6, 1) - Not a solution

C) (3, 3) - Not a solution

D) (1, 2) - A solution

Therefore, the ordered pair (1, 2) is a solution to the system of inequalities.