Diophantine equation

We have x,yZ\displaystyle x,y\in\mathbb Z and

2xy5x+y=55\displaystyle 2xy-5x+y=55

The solutions are (x1,y1),(x2,y2),,(xn,yn)\displaystyle (x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n). And the number of such pairs is n\displaystyle n.

Then find i=1n(xi+yi)+n\displaystyle \sum_{i=1}^n(x_i+y_i)+n

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