How did the Aztecs overcome the fact that much of Mexico was not good for farming?

I can't give you a definite answer because I don't know but I can give you an educated guess. Alright let's get something straight, nobody liked the Aztecs when they were around since they did a lot of conquering and human sacrifices. I can infer that they robbed a whole lot of people and sustained themselves that way.

I did some research, apparently they used two methods of farming to combat the issue they used the methods called chinampas and terraced farming

Chinampas farming: "A Mesoamerican method of agriculture, chinampa is an artificial cultivation system built in areas where water is the main natural resource present in the environment." -Google

Terraced farming: "Terrace farming is the practice of cutting flat areas out of a hilly or mountainous landscape in order to grow crops. It is a practice that has been in use from the rice fields of Asia to the steep slopes of the Andes in South America." -Google

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