Final answer:
The correct pairing is Hernán Cortés with the Aztecs and Francisco Pizarro with the Inka. Cortés conquered the Aztec Empire after entering Tenochtitlan in 1519, and Pizarro defeated the Inka Empire, seizing Cuzco by 1533.
Step-by-step explanation:
Which of the following accurately pairs Spanish conquistadors with the New World empires they destroyed? The correct pair is Hernán Cortés and the Aztecs; Francisco Pizarro and the Inka. Hernán Cortés entered Tenochtitlan in 1519, leading to the fall of the Aztec Empire. Francisco Pizarro, after hearing of riches in the South American continent, went on to capture Cuzco and defeat the Inka Empire by 1533.
The key moment for Cortés was when Tenochtitlan fell to the Spanish under his leadership, whereas for Pizarro, it was the conquest of the Inca Empire after capturing Atahualpa and seizing control of Cuzco. These conquests were motivated by the Europeans' search for gold and silver, which led to terrible consequences for the indigenous populations and the transformation of these empires into Spanish colonies.