# Diophantine equation

Number Theory Level 5

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

Inspiration