# Solve: ax - by = 2ab.

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.

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