How were representatives to the House of Burgesses chosen?

The correct answer is:

They were elected by Virginia landowners.

Explanation:

The House of Burgesses was the first elected legislature in the 13 English colonies in America, it was established in the colony of Virginia, who was previously created by the Virginia Company.

The House of Burgesses was created in 1619, when Royal Governor George Yeardley announced that the Virginia Company had voted in favor of creating a legislative assembly to abolish martial law. The House of Burgesses consisted in Governor George Yeardley, six royally appointed councillors and 22 burgesses who were elected representatives. Only landowners of Virginia could vote in this election.

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