Solve by substitution method

The given system of equations is : \frac{bx}{a} + \frac{ay}{b} = a^{2} + b^{2} . . . (1) x + y = 2 ab . . . . (2) Now, from (2), we get y = 2 ab - x . . . . (3) Now, substituting the value of y from (3) in (1), we get \frac{bx}{a} + \frac{a}{b} \times (2 ab - x) = a^{2} + b^{2} \Rightarrow \frac{bx}{a} + 2 a^{2} - \frac{ax}{b} = a^{2} + b^{2} \Rightarrow \frac{bx}{a} - \frac{ax}{b} = b^{2} - a^{2} \Rightarrow \frac{b^{2} x - a^{2} x}{ab} = b^{2} - a^{2} \Rightarrow \frac{x (b^{2} - a^{2})}{ab} = b^{2} - a^{2} \Rightarrow x = ab Now, from (3), we get y = 2 ab - ab = ab

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