Based on equations reducible to linear equations, Solve for x and y: $6 x + 5 y = 8 x y$ and $8 x + 3 y = 7 x y$

x = 2, y = 2

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x = 1, y = 2

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x = 3, y = 8

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x = 5, y = 7

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Solution

The correct option is B $x = 1, y = 2$

The given equations are
$\Rightarrow 6 x + 5 y = 8 x y . . . . e q (1)$
$\Rightarrow 8 x + 3 y = 7 x y . . . . e q (2)$
$D i v i d e b o t h e q u a t i o n s b y x y$
$\Rightarrow \frac{6}{y} + \frac{5}{x} = 8.... e q (3)$
$\Rightarrow \frac{8}{y} + \frac{3}{1 x} = 7.... e q (4)$
$P u t \frac{1}{x} = u a n d \frac{1}{y} = v i n e q (3) a n d (4)$
$\Rightarrow 6 v + 5 u = 8.... e q (5)$
$\Rightarrow 8 v + 3 u = 7 . . . . e q (6)$
$M u l t i p l y e q (5) b y 3 a n d e q (6) b y 5 a n d s u b t r a c t b o t h$
$\Rightarrow (18 v + 15 u = 24) - (40 v + 15 u = 35)$
$\Rightarrow - 22 v = - 11 \Rightarrow v = \frac{1}{2}$
$P u t v = \frac{1}{2} i n e q (5)$
$\Rightarrow 6 (\frac{1}{2}) + 5 u = 8 \Rightarrow u = 1$
$H e n c e, \frac{1}{x} = u = 1 \Rightarrow x = 1$
$\frac{1}{y} = v = \frac{1}{2} \Rightarrow y = 2$

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