The solution of the pair of equations $$\frac{b}{a}x + \frac{a}{b}y = a^2 + b^2$$​ and x + y = 2ab is:

Given:
​$$\frac{b}{a}x + \frac{a}{b}y = a^2 + b^2 \quad \text{(1)} \\x + y = 2ab \quad \text{(2)} \\$$​​
Formula used:
Solve the pair of linear equations using substitution.
Solution:
From (2): $$\quad y = 2ab - x \quad \text{(i)} \\$$​​
Substitute in (1):
​$$\frac{b}{a}x + \frac{a}{b}(2ab - x) = a^2 + b^2 \\ \ \\\Rightarrow \frac{b}{a}x + \frac{2a^2 - ax}{b} = a^2 + b^2 \\ \ \\\Rightarrow \frac{b}{a}x - \frac{a}{b}x + 2a^2 = a^2 + b^2 \\$$​​
Take all variable terms to one side:
​$$\left( \frac{b}{a} - \frac{a}{b} \right)x = b^2 - a^2 \\$$​​
​$$\Rightarrow \frac{b^2 - a^2}{ab}x = b^2 - a^2 \\\Rightarrow x = ab \\$$​​
Substitute in (i): $$\quad y = 2ab - ab = ab \\$$​​
Correct answer is (b).