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Hamilton-Burr duel have origins in a Senate race of 1791, when Burr defeated Hamilton's father-in-law. Plus, Hamilton was Federalist and Burr were Democratic-Republican.

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Burr ran for President for America. However, Hamilton had other plans for Burr and turned the public against him. As a result, Burr did not win.

He also ran for governor of New York and Hamilton turned the public against Burr again.

That is why they dueled.