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Solve each of the following systems of equations by using the method of cross multiplication :

ax/b – by/a=a+b
ax-by=2ab

$T h e g i v e n e q u a t i o n b e a s, \frac{a}{b} x - \frac{b}{a} y = a + b ...... (1) a x - b y = 2 a b ...... (2) N o w, b y c r o s s m u l t i p l i c a t i o n, w e h a v e, \frac{x}{(- \frac{b}{a}) \times (- 2 a b) - (- b) \times (- a - b)} = \frac{y}{(- a - b) \times a - (- 2 a b) \times \frac{a}{b}} = \frac{1}{\frac{a}{b} \times (- b) - (- \frac{b}{a}) \times a} \Rightarrow \frac{x}{2 b^{2} - a b - b^{2}} = \frac{y}{- a^{2} - a b + 2 a^{2}} = \frac{1}{- a + b} \Rightarrow \frac{x}{b^{2} - a b} = \frac{y}{a^{2} - a b} = \frac{1}{- a + b} \Rightarrow \frac{x}{b (b - a)} = \frac{y}{- a (b - a)} = \frac{1}{(b - a)} \Rightarrow \frac{x}{b} = \frac{y}{- a} = \frac{1}{1} \Rightarrow \frac{x}{b} = \frac{1}{1} a n d \frac{y}{- a} = \frac{1}{1} \Rightarrow x = b a n d y = - a H e n c e, x = b a n d y = - a i s t h e s o l u t i o n o f g i v e n e q u a t i o n .$

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