Given equations are
x + y = 2m …(i)
mx – ny = m2 + n2 …(ii)
From eqn (i), x = 2m – y …(iii)
On substituting x = 2m – y in eqn (ii), we get
⇒ m(2m – y) – ny = m2 + n2
⇒ 2m2 – my – ny = m2 + n2
⇒ – y(m + n) = m2 – 2m2 + n2
⇒ – y(m + n) = – m2 + n2
⇒ y = – (n – m) = m – n
Now, on putting y = m – n in eqn (iii), we get
⇒ x = 2m – (m – n)
⇒ x = 2m – m + n
⇒ x = m + n
Thus, x = m + n and y = m – n is the required solution.