Question

Which point is a solution to this system of inequalities? y ≤ 1 2 ¢ x - 3 y 2 ¢ x > 6?

1) (7,-8)
2) (2,-3)
3) (5,-2)
4) (4,1)

Answer 1

The solutions to the system of inequalities are (2, -3) and (5, -2).

Step-by-step explanation:

To find the solution to the system of inequalities, we need to check which point satisfies both inequalities. The system of inequalities is: y ≤ 1/2x - 3 and y > 6.

We can check each point one by one.

1. For point (7, -8):
2. Plugging in the values, we get -8 ≤ 1/2(7) - 3, which simplifies to -8 ≤ 3. This is false, so (7, -8) is not a solution.
3. For point (2, -3):
4. Plugging in the values, we get -3 ≤ 1/2(2) - 3, which simplifies to -3 ≤ -2. This is true, so (2, -3) is a solution.
5. For point (5, -2):
6. Plugging in the values, we get -2 ≤ 1/2(5) - 3, which simplifies to -2 ≤ -0.5. This is true, so (5, -2) is a solution.
7. For point (4, 1):
8. Plugging in the values, we get 1 ≤ 1/2(4) - 3, which simplifies to 1 ≤ -1. This is false, so (4, 1) is not a solution.

Therefore, the solutions to the system of inequalities are (2, -3) and (5, -2). Option 2) and 3) are correct answers.