Question

Which ordered pairs are solutions to the inequality \(y - 2x \leq -3\)?

A. (1, -5)
B. (-2, 0)
C. (-3, -8)
D. (0, -3)

Answer 1

Ordered pairs A. (1, -5), C. (-3, -8), and D. (0, -3) are solutions to the inequality y - 2x ≤ -3 because when substituted into the inequality, the resulting expressions are either less than or equal to -3.

Step-by-step explanation:

The question asks to determine which ordered pairs are solutions to the inequality y - 2x ≤ -3. To verify if an ordered pair is a solution, each pair's x and y values must be plugged into the inequality.

• If the inequality holds true with the given x and y values, then that ordered pair is a solution.
• If the inequality does not hold true, then that ordered pair is not a solution.

We can test each ordered pair by substituting the x and y values into the inequality:

1. For (1, -5): -5 - 2(1) = -5 - 2 = -7 which is less than -3, so (1, -5) is a solution.
2. For (-2, 0): 0 - 2(-2) = 0 + 4 = 4 which is greater than -3, so (-2, 0) is not a solution.
3. For (-3, -8): -8 - 2(-3) = -8 + 6 = -2 which is greater than -3, so (-3, -8) is a solution.
4. For (0, -3): -3 - 2(0) = -3 which is equal to -3, so (0, -3) is a solution.

Therefore, the ordered pairs that are solutions to the inequality are: A. (1, -5), C. (-3, -8), and D. (0, -3).