An algebra problem by Matheus Yuzawa

Algebra Level 4

In the following equations system: \[\sqrt{x} - \sqrt{y} = log_{3}\frac{y}{x}\] \[2^{x + 2} + 8^{x} = 5 \times 4^{y}\]

How much is \[x + y\]?

This question was taken from IME (Instituto Militar de Engenharia - Brazil) 2014 Entrance Exam.

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