I (0,0)
5(0) + 3(0) <= 2
0 <= 2
true
.
II (-1,0) and (0,-2/3)
5(-1) + 3(0) <= 2
-5 <= 2
true
5(0) + 3(-2/3) <= 2
-2 <= 2
true
.
III (0,2/3) and (1,-2/3)
5(0) + 3(2/3) <= 2
2 <= 2
true
5(1) + 3(-2/3) <= 2
5 - 2 <= 2
3 <= 2
not true
.
Answer: I and II are solutions, (0,2/3) is a solution, but (1,-2/3) is not.