Diophantine equation

We have \(\displaystyle x,y\in\mathbb Z\) and

\[\displaystyle 2xy-5x+y=55\]

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

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

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