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

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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