ANSWER
(4,-4)
EXPLANATION
The given inequality is
[tex]y \geqslant - |x - 4| - 3[/tex]
If (-1,1) satisfies this inequality, then it is a solution.
We substitute x=-1 and y=1 into the inequality to get,
[tex]1 \geqslant - | - 1 - 4| - 3[/tex]
[tex]1 \geqslant - | -5| - 3[/tex]
[tex]1 \geqslant - 5- 3[/tex]
[tex]1 \geqslant - 8[/tex]
This is true. Hence (-1,1) is a solution.
We check for (4,-4) also.
[tex] - 4 \geqslant - |4- 4| - 3[/tex]
[tex]- 4 \geqslant 0 - 3[/tex]
[tex]- 4 \geqslant- 3[/tex]
This is false. Hence (4,-4) is not a solution.
Checking for (-3,2).
[tex] 2 \geqslant - | - 3- 4| - 3[/tex]
[tex]2 \geqslant - | -7| - 3[/tex]
[tex]2 \geqslant - 7 - 3[/tex]
[tex]2 \geqslant - 10[/tex]
This is true. Hence (-3,2) is a solution to the inequality.
Checking for (0,0)
[tex] 0 \geqslant - |0- 4| - 3[/tex]
[tex]0 \geqslant - 4 - 3[/tex]
[tex]0 \geqslant - 7[/tex]
This is true. Hence (0,0) is also a solution.
The correct choice is (4,-4)
