Question

Which ordered pairs are in the solution set of the system of linear inequalities?

y ≥ -1/2x
y < 1/2x + 1
a) (5,-2), (3,1), (-4,2)
b) (5,-2), (3,-1), (4,-3)
c) (5,-2), (3,1), (4,2)

Answer 1

Only the ordered pairs (5,-2) and (3,1) satisfy both inequalities y ≥ -1/2x and y < 1/2x + 1, while (-4,2) does not. Therefore, option A is the correct answer.

Step-by-step explanation:

To find which ordered pairs are in the solution set of the system of linear inequalities y ≥ -1/2x and y < 1/2x + 1, we need to test each ordered pair to see if it satisfies both inequalities.

1. For (5,-2):
   
2. For (3,1):
   
3. For (-4,2):
   

After testing all the ordered pairs, we can conclude that (5,-2) and (3,1) are in the solution set, but (-4,2) is not. Therefore, the correct answer is option A: (5,-2), (3,1).