Question

Which ordered pair makes both inequalities true:

{ y=−x+1,y≤x}
A. (-3, 5)
B. (-2, 2)
C. (-1, -3)
D. (0, -1)

Answer 1

The only ordered pair that makes both inequalities true is option D (0, -1), as it is the only one that satisfies both y = -x + 1 and y ≤ x when the values are substituted into the equations.

Step-by-step explanation:

To identify which ordered pair makes both inequalities y = -x + 1 and y ≤ x true, we need to test each option separately.

1. For option A (-3, 5), substituting -3 for x and 5 for y in the equation y = -x + 1 gives 5 = -(-3) + 1, which simplifies to 5 = 3 + 1. This is not true, so option A does not satisfy the first inequality.
2. Option B (-2, 2) gives 2 = -(-2) + 1, which simplifies to 2 = 2 + 1. This is also false.
3. Option C (-1, -3), when substituted in, gives -3 = -(-1) + 1 which simplifies to -3 = 1 + 1. This does not hold true.
4. Lastly, for option D (0, -1), when we substitute, we get -1 = -(0) + 1, which is true since -1 = 1. And for the inequality y ≤ x, we have -1 ≤ 0, which is also true.

Therefore, the only ordered pair that satisfies both inequalities is option D, which is (0, -1).