Final answer:
Parallel implementation is the method of system implementation that requires both the previous system and the new system to perform identical tasks at the same time.
Step-by-step explanation:
The method of system implementation that requires both the previous system and the new system to perform identical tasks at the same time is called Parallel implementation. In this approach, the old and new systems operate simultaneously, allowing for a comparison of results and ensuring a smooth transition. This method helps to minimize the risks and disruptions associated with implementing a new system by allowing for a gradual switch from the old system to the new one.