Solve the following system of equations by substitution method:

, a ≠ 0, b ≠ 0

ax – by = a² – b²

Given equations are

…(i)

ax – by = a² – b² …(ii)

eqⁿ (i) can be re – written as,

⇒ bx + ay = ab×2

⇒ bx + ay = 2ab

…(iii)

On substituting in eqⁿ (ii), we get

⇒ 2a² b – a² y – b² y = b(a² – b²)

⇒ 2a² b – y(a² + b² ) = a²b – b³

⇒ – y(a² + b² ) = a² b – b³ – 2a²b

⇒ – y(a² + b² ) = – a²b – b³

⇒ – y(a² + b² ) = – b(a² + b²)

Now, on putting y = b in eqⁿ (iii), we get

⇒ x = a

Thus, x = a and y = b is the required solution.