Question

Which point would not be a solution to the system of linear inequalities shown below? y ≥ -1/3x + 8, y ≤ 2x + 1

1) (-1, 0)
2) (0, 2)
3) (3, 5)
4) (4, 3)

Answer 1

To determine which point is not a solution to the system of linear inequalities, we substitute the x and y values of each point into both inequalities. The point (-1, 0) is not a solution to the system of linear inequalities.

Step-by-step explanation:

To determine which point is not a solution to the system of linear inequalities, we substitute the x and y values of each point into both inequalities. If the inequalities are not satisfied, the point is not a solution. Let's check each point:

1. (-1, 0): Substitute x = -1 and y = 0 into both inequalities. The first inequality becomes y ≥ -1/3(-1) + 8, which simplifies to y ≥ 8. This is true. The second inequality becomes y ≤ 2(-1) + 1, which simplifies to y ≤ -1. This is not true, so (-1, 0) is not a solution to the system of linear inequalities.
2. (0, 2): Substitute x = 0 and y = 2. The first inequality becomes y ≥ -1/3(0) + 8, which simplifies to y ≥ 8. This is true. The second inequality becomes y ≤ 2(0) + 1, which simplifies to y ≤ 1. This is true. Therefore, (0, 2) is a solution to the system of linear inequalities.
3. (3, 5): Substitute x = 3 and y = 5. The first inequality becomes y ≥ -1/3(3) + 8, which simplifies to y ≥ 7. This is true. The second inequality becomes y ≤ 2(3) + 1, which simplifies to y ≤ 7. This is true. Therefore, (3, 5) is a solution to the system of linear inequalities.
4. (4, 3): Substitute x = 4 and y = 3. The first inequality becomes y ≥ -1/3(4) + 8, which simplifies to y ≥ 7.33. This is true. The second inequality becomes y ≤ 2(4) + 1, which simplifies to y ≤ 9. This is true. Therefore, (4, 3) is a solution to the system of linear inequalities.

Based on the above calculations, the point that would not be a solution to the system of linear inequalities is (-1, 0).