Final answer:
The fighting between British soldiers and the Massachusetts militiamen, the minutemen, began in Lexington and Concord in Massachusetts.
Step-by-step explanation:
The two places where the fighting broke out between British soldiers and the Massachusetts militiamen, the minutemen, signaling the start of the American Revolution, were Lexington and Concord in Massachusetts. At Lexington, a shot rang out and the war began almost as an accident. The British army retreated back to Boston with gunfire skirmishes occurring along the way.