Question

which ordered pairs make both inequalities true? choose two answers.
y < 5x + 2
y ≥ \frac{1}{2}x + 1
(0, 2)
(2, -1)
(2, 2)

Explanation:

Step1: Test (0,2) in inequalities

First inequality: $2 < 5(0)+2 \implies 2 < 2$ (False)
Second inequality: $2 \geq \frac{1}{2}(0)+1 \implies 2 \geq 1$ (True)
Pair fails one inequality.

Step2: Test (2,-1) in inequalities

First inequality: $-1 < 5(2)+2 \implies -1 < 12$ (True)
Second inequality: $-1 \geq \frac{1}{2}(2)+1 \implies -1 \geq 2$ (False)
Pair fails one inequality.

Step3: Test (2,2) in inequalities

First inequality: $2 < 5(2)+2 \implies 2 < 12$ (True)
Second inequality: $2 \geq \frac{1}{2}(2)+1 \implies 2 \geq 2$ (True)
Pair satisfies both inequalities.

(Note: Assuming a fourth option is missing, but from provided pairs, (2,2) is valid. To match the "choose two" instruction, we can infer if we consider the graph: the overlapping region is above the solid line and below the dashed line. Another valid pair would be (1,2):
Test (1,2):
First inequality: $2 < 5(1)+2 \implies 2 <7$ (True)
Second inequality: $2 \geq \frac{1}{2}(1)+1 \implies 2 \geq 1.5$ (True)
But since it's not listed, we use the given valid pair and note, but from provided options, (2,2) is valid, and if we assume the full set, but based on given visible pairs, we proceed with the valid one and clarify.)

Answer:

(2, 2)
(Note: A second valid pair is not fully visible in the image, but from the provided options, (2,2) is confirmed valid. A second valid pair would be one that lies in the overlapping region above $y=\frac{1}{2}x+1$ and below $y=5x+2$, e.g., (1,2) if it were an option.)