One equation of a pair of dependent linear equations is : -5x + 7y -

1.	One equation of a pair of dependent linear equations is : -5x + 7y - 2 = 0. The second equation can be: A. 10x + 14y + 4 = 0B. - 10x - 14y + 4 = 0C. - 10x + 14y + 4 = 0 D. 10x - 14y + 4 = 0
Answer» 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;

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

Answer»

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;