To determine which point is a solution to the system of linear inequalities y ≤ -3x - 2 and y > x - 2, we can test each point by substituting the x and y values into both inequalities.
Let's start with point A (-4, 4):
y ≤ -3x - 2
4 ≤ -3(-4) - 2
4 ≤ 10
This is false, so (-4, 4) is not a solution to the first inequality.
y > x - 2
4 > -4 - 2
4 > -6
This is true, so (-4, 4) is a solution to the second inequality.
Since (-4, 4) satisfies only one of the two inequalities, it is not a solution to the system of linear inequalities.
Now let's test point B (4, 4):
y ≤ -3x - 2
4 ≤ -3(4) - 2
4 ≤ -14
This is false, so (4, 4) is not a solution to the first inequality.
y > x - 2
4 > 4 - 2
4 > 2
This is true, so (4, 4) is a solution to the second inequality.
Since (4, 4) satisfies only one of the two inequalities, it is not a solution to the system of linear inequalities.
Therefore, neither point A nor point B is a solution to the system of linear inequalities y ≤ -3x - 2 and y > x - 2.