Final answer:
To find which point is a solution to the system of linear inequalities y ≥ −x − 4 and y < 2x − 2, we can substitute the x and y values of each option into the inequalities. Only option (c), (-4, -7), satisfies both inequalities and is therefore a solution.
Step-by-step explanation:
To find which point is a solution to the system of linear inequalities, we need to check if the point satisfies both inequalities. Let's start with option (a), (-1, 4):
Substituting the x and y values into the inequalities:
- -1 ≥ -(-1) - 4 which simplifies to -1 ≥ 3, which is false.
- 4 < 2(-1) - 2 which simplifies to 4 < -4, which is also false.
Since option (a) does not satisfy both inequalities, it is not a solution to the system of linear inequalities. We can continue checking the other options using the same process.
Option (b), (-10, 3):
-10 ≥ -(-10) - 4 which simplifies to -10 ≥ 6, which is false.
3 < 2(-10) - 2 which simplifies to 3 < -22, which is false.
Option (c), (-4, -7):
-4 ≥ -(-4) - 4 which simplifies to -4 ≥ 0, which is true.
-7 < 2(-4) - 2 which simplifies to -7 < -10, which is true.
Option (d), (9, 9):
9 ≥ -(9) - 4 which simplifies to 9 ≥ -13, which is true.
9 < 2(9) - 2 which simplifies to 9 < 16, which is true.
Therefore, the point (-4, -7) would be a solution to the system of linear inequalities.