The Federal Judiciary Act of 1789 complemented the US Constitution by:
1. Describing how the federal courts operating under the Supreme Court would be set up: This act established the federal court system, outlining the structure and jurisdiction of the federal judiciary. It created the district and circuit courts, setting the framework for how cases would be heard and appealed at different levels within the federal system.
2. Giving the Supreme Court checks and balances over the other two branches of government: The Act also outlined the powers and responsibilities of the Supreme Court, ensuring that it would serve as a check on the executive and legislative branches. By establishing the Supreme Court's authority to interpret the Constitution and federal laws, it helped balance the powers among the branches of government as envisioned in the Constitution.