Question

Which of the following points is a solution to y≤−2x+3?

a) (0, 4)
b) (1, 0)
c) (3, -2)
d) (5, -2)

Answer 1

The solutions to the inequality y ≤ -2x + 3 are (1, 0), (3, -2), and (5, -2).

Step-by-step explanation:

To determine which point is a solution to the inequality y ≤ -2x + 3, we can substitute the coordinates of each point into the inequality and see if the inequality holds true.

a) (0, 4): Substitute x = 0 and y = 4 into the inequality gives 4 ≤ -2(0) + 3 or 4 ≤ 3. This is not true, so (0, 4) is not a solution.

b) (1, 0): Substitute x = 1 and y = 0 into the inequality gives 0 ≤ -2(1) + 3 or 0 ≤ 1. This is true, so (1, 0) is a solution.

c) (3, -2): Substitute x = 3 and y = -2 into the inequality gives -2 ≤ -2(3) + 3 or -2 ≤ -3. This is true, so (3, -2) is a solution.

d) (5, -2): Substitute x = 5 and y = -2 into the inequality gives -2 ≤ -2(5) + 3 or -2 ≤ -7. This is true, so (5, -2) is a solution.

Therefore, the solutions to the inequality y ≤ -2x + 3 are (1, 0), (3, -2), and (5, -2).