Find the separate equation of the lines represented by the following equation.
$3 x^{2} - 10 x y - 8 y^{2} = 0$ .

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Solution

$3 x^{2} - 10 x y - 8 y^{2} = 0$
$3 x^{2} - 12 x y + 2 x y - 8 x^{2} = 0$
$3 x (x - 4 y) + 2 y (x - 4 y) = 0$
$(x - 4 y) (3 x + 2 y) = 0$
Separated equations
$x - 4 y = 0$ and
$3 x + 2 y = 0$

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