Under the electoral law at that time, the president and vice president were not elected separately, the candidate with the most votes would become the president, and the runner-up would be the vice president. However, when counting votes, the votes of Mr. Jefferson and Mr. Burr were equal.
At this point, the US House of Representatives has to settle. The US House of Representatives is made up of the majority of those belonging to the Federal Party. They preferred Mr. Burr, because they thought that Burr was easier to control than Mr. Jefferson. But Mr. Hamilton used his influence to make the majority of the Union members support Mr. Jefferson.
The final vote took place on February 17, 1801, resulting in Mr. Jefferson becoming President and Mr. Burr as Vice President. However, after that, Mr. Jefferson did not choose Mr. Burr, but chose New York Governor George Clinton as the vice presidential candidate when running for the second presidency in 1804.