Question

Question 9
One equation of a pair of dependent linear equations is - 5x + 7y – 2 = 0
(A) 10x + 14y + 4 = 0
(B) –10x – 14y + 4 = 0
(C) –10x + 14y + 4 = 0
(D) 10x – 14y = –4​​​​​​​

Answer 1

Condition for dependent linear equations
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{k}$
Given equation of line is – 5x + 7y – 2 = 0
Here, $a_1=-5,b_1=7,c_1=-2$
$FromEq.\left(i\right)-\frac{5}{a_2}=\frac{7}{b_2}=-\frac{2}{c_2}=\frac{1}{k}\Rightarrow a_2=-5k,b_2=7k,c_2=-2k$
Where, k is any arbitrary constant
Putting k = 2, then $a_2=-10,b_2=14$
And $c_2=-4$
$\therefore$ The required equation of line becomes
$a_{2}x+b_{2}y+c_2=0$
$\Rightarrow$ -10x + 14y – 4 = 0
$\Rightarrow$ 10x – 14y + 4 = 0