Question

I NEED HELP!!!!!!!!!!!! FAST!!!!!

On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system.

y ≥ 3x + 2


A. Region B

B. Region C

C. Region A

D. Region D

Answer 1

From the graph, we know the y-intercepts (look at the picture).

y = 2 → y = 3x + 2

y = 3 → y = -1/3x + 3

We have

y ≥ 3x + 2 (shadow up of a line)

y ≤ -1/3x + 3 (shadows down of a line)

the common region is D.

Answer: D. Region D.

Answer 2

Option (a) and (d) are correct.

region A and region D satisfies the given inequality y ≥ 3x + 2.

Explanation:

Given : The graph of the system of inequalities y ≥ 3x + 2.

We have to determine which region contains the solution to the system.

We will chose a test point in each region and see which point satisfies the given inequality.

For region A)

(0,6) is in region A

Put x = 0 and y = 6 in given inequality

We get,

6 ≥ 3(0) + 2.

6 ≥ 2 (True)

For region B)

(4,6) is in region B

Put x = 4 and y = 6 in given inequality

We get,

6 ≥ 3(4) + 2.

6 ≥ 12 + 2 = 14 (False)

For region C)

(0,0) is in region C

Put x = 0 and y = 0 in given inequality

We get,

0 ≥ 3(0) + 2.

0 ≥ 2 (False)

For region D)

(-2,2) is in region A

Put x = -2 and y = 2 in given inequality

We get,

2 ≥ -3(2) + 2.

2 ≥ -6+ 2 = -4 (True)

Thus, region A and region D satisfies the given inequality

Thus, Option (a) and (d) are correct.