Who was given the authority to set up a system of federal courts?

Congress has the authority to set up the system of federal courts.

Explanation:

The "United States Constitution" has established only "one" federal court, which is the "Supreme Court" of United States. The Constitution defines what will be the structure of the legislative branch of the government and how it will function. It directs the President's responsibilities and powers.

“Article III of the Constitution” gave the power to ordain and set up lower federal courts to the Congress.  It also manages the judicial decisions taken by the federal government. President appointed nine justices of “U.S. Supreme Court” along with the Senate's approval.

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