The modern united states regime shares power between the states and national government, makin it an example of which type of system?

The correct answer is - federal system.

The United States are a country in which the federal system is the one in place. This system practically means that the power is shared between the central government and the federal states. The central government is still the dominant center of power, but the federal states also are able to function in a manner they want to, to a certain level of course. The reason why is this type of power in force in the United States is mainly because the country has become what it is with the unification of the states. There's 52 federal states in the United States, and most of them were self governed in big portion of the American history, so when they decided to create one big country, the condition was that they still have power in the federal states.

the social contract theory