Find the joint equation of the following pair of lines :
$2 x + y = 0 and 3 x - 5 y = 0$

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Solution

soln :
Eqn of first line $\Rightarrow 2 x + y = 0$
Eqn of second line $\Rightarrow 3 x - 5 y = 0$
Thus the joint equations of a line is gn by
$(2 x + y) (3 x - 5 y) = 0$
$2 x (3 x - 5 y) + y (3 x - 5 y) = 0$
$6 x^{2} - 10 x y + 3 x y - 5 y^{2} = 0$
$∴ 6 x^{2} - 7 x y - 5 y^{2} = 0$
This is the required joint eqn

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