Question

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)

Answer 1

B

Explanation:

(5,-2)

Answer 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.
Answer:
A point that lies in the solution set to the system of inequalities is:
(5, -2)