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Given: … (1)

ax - by = 2ab … (2)

Multiplying by ab to (1) and a to (2), we get

a²x – b²y = a²b + ab² … (3)

a²x – aby = 2a²b … (4)

Subtracting equation (4) from equation (3),

(a²x – a²x) + ( - aby) – ( - b²y) = (2a²b - a²b) – ab²

⇒ - aby + b²y = a²b – ab²

⇒ by(b – a) = ab(a – b)

⇒ y = b(b – a) / ab(a – b)

⇒ y = - a

Substitute y value in (2),

ax – b( - a) = 2ab

⇒ ax + ab = 2ab

⇒ ax = ab

⇒ x = b

The solution is x = b and y = - a.