Question

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Answer 1

Answer:

Option (a) and (d) are correct.

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

Step-by-step 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.

Answer 2

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.