Question

Which point lies in the solution set for the following system of inequalities?
y < 2x + 4
y < -2x + 2

(1, 0)
(-5, -2)
(0, -3)
(-1, 5)

Answer 1

Test each point in both inequalities.
The point that makes both inequalities true is the answer.

Answer 2

Can u show me?

Answer 3

Let's try the first point.

Choice A: (1, 0)
The x-coordinate is 1, and the y-coordinate is 0.
We replace x with 1 and y with 0.

y < 2x + 4
0 < 2(1) + 4
0 < 2 + 4
0 < 6
This is a true statement, so the first choice works on the first inequality.
Now we need to test the first choice in the second inequality.

y < -2x + 2
0 < -2(1) + 2
0 < -2 + 2
0 < 0
This is not true. The first choice does not work on the second inequality. That means the first choice is not the answer.

Answer 4

Now do the same to the other choices.