Question

One equation of a pair of dependent linear equations is -5x +7y = 2. the second equation can be :

(A) 10x +14y +4 = 0
(B) -10x -14y +4 =0
(C) 10x - 14y = -4​

Answer 1

Option (C) is correct.

$\large{\underline{\sf{\red{Explanation :}}}}$

$\displaystyle{\sf{ \dfrac{a_{1}}{a_{2}} = \dfrac{b_{1}}{b_{2}} = \dfrac{c_{1}}{c_{2}} = \dfrac{1}{k}}}$ ____(i)

Given equation of line is, $\displaystyle{\sf{ -5x+7y-2=0}}$

Here, $\displaystyle{\sf{ a_{1} = -5, b_{1} = 7, c_{1} = -2}}$

From Eq.(i), $\displaystyle{\sf{ \dfrac{-5}{a_{2}} = \dfrac{7}{b_{2}} = \dfrac{-2}{c_{2}} = \dfrac{1}{k}}}$

$\implies{\sf{ a_{2} = -5k, b_{2} = 7k, c_{2} = -2k}}$

Where,k is any arbitrary constant.

Putting k = 2, then ${\sf{ a_{2} = -10, b_{2} = 14, c_{2} = -4}}$

$\therefore$ The required equation of line becomes,

• $\displaystyle{\sf{ a_{2}x + b_{2}y + c_{2} =0}}$

$\implies{\sf{ -10x +14y - 4 = 0}}$

$\large\implies{\boxed{\sf{\orange{ 10x -14y + 4 = 0\: or\: 10x-14y =-4}}}}$

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