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Question 4(Multiple Choice Worth 1 points)

(05.06 MC)
The following inequalities form a system.
yz²x+1
y<--x+2
Which ordered pair is included in the solution to this system?
(-6, 3.5)
(-6, -3)
(-4,3)
(-4,4)

1 Answer

4 votes

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).

User Deepika Patel
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