Solve the following system of equations by substitution method:

x + y = 2ab

Given equations are

…(i)

x + y = 2ab …(ii)

eqⁿ (i) can be re - written as,

⇒ b² x + a² y = ab × (a² + b²)

…(iii)

Now, from eqⁿ (ii), y = 2ab – x …(iv)

On substituting y = 2ab – x in eqⁿ (iii), we get

⇒ b² x = b³ a – a³b + a²x

⇒ b²x – a²x = b³a – a³b

⇒ (b^{2 –} a²) x = ab(b² – a²)

⇒ x = ab

Now, on putting x = ab in eqⁿ (iv), we get

⇒ y = 2ab – ab

⇒ y = ab

Thus, x = ab and y = ab is the required solution.