Step-by-step explanation:
The administration that took office on March 4, 1797, had a Federalist President, John Adams, and a Republican Vice President, Thomas Jefferson, because of the way that the U.S. presidential election process worked at the time.
In the 1796 presidential election, the two main political parties were the Federalist Party and the Democratic-Republican Party (which later became known simply as the Republican Party). John Adams, a Federalist, ran against Thomas Jefferson, a Republican. At that time, the candidate who received the most electoral votes became president, and the candidate who received the second-most electoral votes became vice president.
In the 1796 election, John Adams received the most electoral votes, and Thomas Jefferson received the second-most electoral votes. Therefore, according to the rules of the time, Adams became president and Jefferson became vice president, even though they were from different political parties.
This system of electing the president and vice president led to some issues, particularly when the president and vice president were from different political parties. Adams and Jefferson had different political views and often disagreed on important issues, which made governing difficult. The system was eventually changed by the 12th Amendment to the U.S. Constitution, which was ratified in 1804, and which established separate ballots for the president and vice president.