Question

One equation of a pair of dependent linear equations is :  -5x + 7y - 2 = 0. The second equation can be: 

A. 10x + 14y + 4 = 0

B. - 10x - 14y + 4 = 0

C. - 10x + 14y + 4 = 0 

D. 10x - 14y + 4 = 0

Answer 1

D. 10x - 14y + 4 = 0

Condition for dependent linear equations -

a₁ /a₂ = b₁/b₂ = c₁/c₂ …(i)

Given equation of line is, - 5x + 7y - 2 = 0;

Comparing with ax+ by +c = 0;

Here, a₁ = - 5, b₁ = 7, c₁ = - 2;

For second equation, let’s assume a₂x + b₂y + c₂ = 0;

From Eq. (i), -5/a₂ = 7/b₂ = -2/c₂ = 1/k

Where, k is any arbitrary constant.

Putting k = - 1/2 then

a₂ = 10, b₂ = - 14, c₂ = 4;

∴ The required equation of line becomes

a₂x + b₂y + c₂ = 0;

10x - 14y + 4 = 0;