Final answer:
The correct answer is option B. No solutions.
Step-by-step explanation:
To determine the number of solutions a system of equations has, we need to solve the system and see if we get a unique solution, no solution, or infinitely many solutions.
Let's solve the system of equations:
5x - y = 2
5x - y = -2
To do this, we can subtract the second equation from the first:
(5x - y) - (5x - y) = 2 - (-2)
0 = 4
Since the equation 0 = 4 is not true, this means there are no solutions to the system. Therefore, the correct answer is B. No solutions.