# An algebra problem by Rahil Sehgal

Algebra Level 4

$\large \begin{cases} 2^{y-x}(x+y) = 1 \\ (x+y)^{x-y} =2 \end{cases}$

Let $$(x_1, y_1), (x_2, y_2) , \ldots , (x_n , y_n)$$ denote all the solutions of $$(x,y)$$ that satisfy the system of equations above.

Find $$\displaystyle \sum_{i=1}^n (x_n + y_n)$$ to 3 decimal places.

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