Given equations are
x + y = a – b …(i)
ax – by = a2 + b2 …(ii)
From eqn (i), x = a – b – y …(iii)
On substituting x = a – b – y in eqn (ii), we get
⇒ a(a – b – y) – by = a2 + b2
⇒ a2 – ab – ay – by = a2 + b2
⇒ – ab – y(a + b) = b2
⇒ – y(a + b) = b2 + ab
Now, on putting y = – b in eqn (iii), we get
⇒ x = a – b – ( – b)
⇒ x = a
Thus, x = a and y = – b is the required solution.