Solve for x and y :

mx - ny = m² + n²

x - y = 2n.

I Equation:

mx - ny = m² + n²

II Equation:

x - y = 2n

=> m(x - y) = m(2n) [Multiplying both sides by m]

=> mx - my = 2mn [Let it is III Equation]

Subtract III Equation from I Equation:

(mx - ny) - (mx - my) = (m² + n²) - 2mn

=> mx - ny - mx + my = m² - 2mn + n²

=> my - ny = (m-n)²

=> y(m-n) = (m-n)²

=> y = (m-n)²/(m-n)

=> y = m - n

By putting y = (m-n) in II Equation, we get:

x - (m-n) = 2n

=> x = 2n + (m-n)

=> x = 2n + m - n

=> x = m + n