Forming the U.S, A system was developed in which both the federal government and the states had powers. What kind of system is this called?

The system you are referring to is called federalism. Federalism is a system of government in which power is divided and shared between a central authority (the federal government) and regional authorities (the states). In the case of the United States, the U.S. Constitution grants certain powers to the federal government while reserving other powers to the individual states. This division of powers allows for a balance of power between the national government and the states. It is important to note that federalism can take different forms in different countries, depending on their specific constitutional arrangements.