Question

Which ordered pairs make both inequalities true? Check all that apply.

Answer 1

When an inequality is true it is in the region that both are shaded, so the answer would be 1,1 and 2,2

Answer 2

Answer: The pair (2, 2)

Step-by-step explanation:

The inequalities that we have are:

y ≥ (1/5)x + 1

y < 2x + 1

Now, let's try the options:

Notice that the pairs that make bot inequalities true are pairs that lie in the region where we have both colors (blue and orange)

Those options will be the pairs (1,3) and (2,2)

now, let's prove if those numbers work for our inequalities.

(1,3)

3 ≥ (1/5)*1 + 1 = 6/5  true

3 < 2*1 + 1 = 3 false

here we have a problem, while the pair (1,3) lies in the region, it lies exactly in the doted line of the second inequality, this means that this pair does not work for the second inequality.

now, let's test the other option.

(2, 2)

2 ≥ (1/5)*2 + 1  =7/6 true

2 < 2*2 + 1 = 5 true

the correct option is the pair (2, 2)