ANSWER
(-5,1) is the correct answer
EXPLANATION
The given inequality is:
[tex]y \: > \: |x|- 6[/tex]
If any point satisfies this inequality, then it is a solution.
We need to substitute each point into the given inequality.
We substitute (-5,1) to get:
[tex]1\: > \: | - 5|- 6 \implies1\: > \: - 1[/tex]
This statement is true. Hence (-5,1) is a solution.
For (-1,-5), we have
[tex] - 5\: > \: | - 1|- 6 \implies - 5\: > \: - 5[/tex]
This is false.
For (5,-1), we have
[tex] - 1\: > \: | 5|- 6 \implies - 1\: > \: - 1[/tex]
This is also false.
