Answer:
answer is (C).
Explanation:
Substituting y = -x + 2 from the second inequality into the first inequality, we get:
z^2x + 1 < (-x + 2)z^2
Rearranging, we get:
z^2(x + 1) < (-x + 2)z^2 - 1
Dividing both sides by z^2, and noting that z^2 > 0, we get:
x + 1 < (-x + 2) - 1/z^2
Simplifying, we get:
2x < -1/z^2
x < -1/(2z^2)
Therefore, for any value of z, the solution set of the system is the set of all ordered pairs (x, y) where x < -1/(2z^2) and y < -x + 2.
Checking each of the answer choices:
(-6, 3.5): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.
(-6, -3): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.
(-4, 3): In the solution set, since -4 is less than -1/(2z^2) for any value of z, and 3 is less than -(-4) + 2 = 6.
(-4, 4): Not in the solution set, since -4 is not less than -1/(2z^2) for any value of z.
Therefore, the ordered pair included in the solution set is (-4, 3), and the answer is (C).