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)

For this case we will evaluate each point separately in the given functions.
 We have then:
 For (-5, 2):
 y ≤ x - 5
 2 ≤ -5 - 5
 2 ≤ -10
 The point does not comply with the system of equations:
 For (5, -2)
 y ≤ x - 5
 -2 ≤ 5 - 5
 -2 ≤ 0
 We verify the other inequality:
 y ≥ -x - 4
 -2 ≥ -5 - 4
 -2 ≥ -9
 The point complies with the system of equations.
 
 A point that lies in the solution set to the system of inequalities is:
 (5, -2)

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