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.
