basic algebra with several variables-why won't it work?

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You are using "implicit multiplication" which Sage does not understand by default (you can turn it on if you want). You should change 2y above to 2*y and 80(3200-x-y) to 80*(3200-x-y), etc... Here is code that works:

x, y = var('x, y')
solve([20*(6400-x-2*y)==0, 80*(3200-x-y)==0], x, y)

Sage's output is:

[[x == 0, y == 3200]]

ps. Implicit multiplication can be turned on using: implicit_multiplication(True), see the preparser documentation.