Question

Which of the following points lie in the solution set to the following system of inequalities?

y ≤ x − 5

y ≥ −x − 4


A. (−5, 2)

B. (5, −2)

C. (−5, −2)

D. (5, 2)

Answer 1

B. (5, -2)

Explanation:

Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.

A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false

B. -2 ≤ 5 -5 . . . true

... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice

C. we know from A that the first inequality will be satisfied

... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false

D. 2 ≤ 5 -5 . . . . false