Question

Which ordered pair is a solution to the system of inequalities?

y > –x
y ≤ x + 1

A) (0,5)

B) (4,–1)

C) (1,3)

D) (–4,0)

Answer 1

Answer: Choice B. (4, -1)

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Step-by-step explanation:

Choice A can be ruled out because

`y \le x+1\\\\5 \le 0+1\\\\5 \le 1\\\\`

which is false.

Choices C and D are similar, so they can be ruled out as well.

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Choice B is the answer because it makes both inequalities true.

If we plug the coordinates of (4,-1) into the first inequality, we get

`y > -x\\\\-1 > -4`

which is a true statement because -1 is to the right of -4 on the number line.

Now try the other inequality

`y \le x+1\\\\-1 \le 4+1\\\\-1 \le 5\\\\`

that's true also. So again, (4,-1) makes both inequalities true, and that's why choice B is the answer.

Answer 2

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Answer:

B) (4,–1)

Step-by-step explanation:

A graph can help you figure this out. The point (4, -1) is in the doubly-shaded area, so is a solution to this system.