No, they cannot coexist - not in the sense most people mean, anyways.

Equality, as most people consider it, is knocking everyone down the same playing field, forcing the great to be mediocre, and letting everything stagnate. But people are not equal. Minds are not equal. There is a social system designed around equality: communism.

Freedom is, as I see it, the ultimate equality - the equality of the mind. You are judged on your own merits, and your own mind. You are free to excel as far as your mind and your efforts are able. The people who want to stagnate can stagnate, but cannot leech off the rest. There is a social system designed around freedom: capitalism.

Do you think capitalism and communism can coexist?