One equation of a pair of dependent linear equations is \( -5 x+7 y=2 \). The second equation can be
(A) \( 10 x+14 y+4=0 \)
(B) \( -10 x-14 y+4=0 \)
(C) \( -10 x+14 y+4=0 \)
,b>(D) \( 10 x-14 y=-4 \)

Given:

One equation of a pair of dependent linear equations is \( -5 x+7 y=2 \).

To do:

We have to find the second equation.

Solution:

We know that,

The condition for dependent linear equations is,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{k}$

 \( -5x+7y-2=0 \)

Here,

$a_1=-5, b_1=7, c_1=-2$

For $k=2$,

$a_2=2(-5)=-10, b_2=2(7)=14, c_2=2(-2)=-4$

Therefore,

The required dependent linear equation is $a_2x+b_2y+c_2=0$, i.e., $-10x+14y-4=0$

$\Rightarrow 10x-14y+4=0$

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Updated on: 10-Oct-2022

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