Which system of government did the Constitution create in the United States?

The Constitution provided a federal system of government in reaction to the earlier Articles of Confederation. Both documents were attempts to unify the newly-formed United States which were anything but united.
The Articles were shelved due to a lack of enforcement in bringing the new states together with a national mindset. Many in the Constitutional Convention felt that without a strong, central government, the new country could not withstand attacks from outside or strife from within.
Some states refused to accept the federal government structure of an executive, legislative and judicial branches without some safeguards for individuals. They had fought against a king with absolute power and were leery of establishing a government with that same potential. To appease those states and to gain ratification of the Constitution, the Bill of Rights was added. These 10 amendments gave protection from federal domination over individuals and states. Initially, the Bill of Rights only applied to federal laws and regulations but were later applied to state and local laws through rulings of the Supreme Court of the United States.

In the United States, the Constitution created a federal system of government. The federal system is a decentralized one. It divides the power of governance between a federal government and various state governments. 
The Constitution bequeaths the status of "dual sovereignty" to both the federal and state governments. The Tenth Amendment essentially defines how power is balanced between the federal and state governments in the United States. It proclaims that the federal government is constrained by its enumerated powers in the Constitution. It cannot overstep those boundaries. Thus, any powers not assigned to it are retained by the states.
The federal government oversees matters of national concern, while the state governments address local issues. The Constitution allows the federal government (through Congress) to print money, levy taxes, declare war, and regulate interstate commerce. In matters of national security or the national defense, the federal government has jurisdiction. State governments, however, can determine how each state addresses local issues.
For more, please refer to the link below.
https://www.law.cornell.edu/wex/federalism