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Derivative from First Principle

If ax+by=a ...

Question

If $a x + b y = a^{2} - b^{2}$ and $b x + a y = 0$ find the value of $(x + y)$

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Solution

$b x + a y = 0 \Rightarrow y = \frac{- b x}{a}$
$a x + b y = a^{2} - b^{2} \Rightarrow a x - \frac{b^{2} x}{a} = a^{2} - b^{2}$
$\Rightarrow (a^{2} - b^{2}) x = a (a^{2} - b^{2}) \Rightarrow x = a$
$y = \frac{- b}{a} (a) \Rightarrow y = - b \Rightarrow x + y = a - b$

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