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

y ≤ x − 5
y ≥ −x − 4

(−5, 2)
(5, −2)
(−5, −2)
(5, 2)

Second option : (5, −2)

Step-by-step explanation: Given system of inequalities

y ≤ x − 5

y ≥ −x − 4

Plugging x=5 and y=-2 in first inequality

-2  ≤ 5 − 5

-2 ≤  0 : True.

Plugging x=5 and y=-2 in second inequality

-2 ≥ −5 − 4

-2 ≥ -9 : Also true.

Point  (5, −2) satisfied both of the given inequalities in the system.

Therefore, (5,-2) is correct option.