Solve the following pair of equations by reducing them to a pair of linear equations$ 6 x+3 y=6 x y $
$2 x+4 y=5 x y $

Given:$6x + 3y = 6xy$....i)

            $2x + 4y = 5xy$...(ii)

To do:  Solve the given pair of equation by reducing them to a pair of linear equation.

Solution:

Dividing (i) and (ii) by $ xy$

$\frac{6}{y}$ + $\frac{3}{x}$ = 6...(iii)

$\frac{2}{y} + \frac{4}{x}$ = 5....(iv)

$3 x$ (iv)  $\frac{6}{y} $+$ \frac{12}{x}$ = 15

           (iii)   $\frac{6}{y}$ + $\frac{3}{x}$ = 6.

Subtracting  $\frac{9}{x}$ = $9$ or $x = 1$

Substituting $x = 1$ in (iii)

$\frac{6}{y}$ + $\frac{3}{1}$ = 6 or $\frac{6}{y}$ = 3$

$y = \frac{6}{3}$ = 2

So, $x = 1 and y = 2$ is answer

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Updated on: 10-Oct-2022

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