Unknowns are Unknowns! (Part 2)

Algebra Level 3

\[\large \begin{cases} 2x^2 + 2y^2 = 5xy \\ \dfrac{x-y}{x+y} = \dfrac{a}{b} \end{cases}\]

Real numbers \(x\), \(y\), \(a\), and \(b\), where \(a\) and \(b\) are positive coprime integers, satisfy the system of equations above. Find \(a \times b - a + b \div a\).