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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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