Solve the following pair of linear equations by substitution method:

x + y = 2m

mx — ny = m² + n²

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.