Question

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

Options

• 10x + 14y + 4 = 0

• –10x – 14y + 4 = 0

• –10x + 14y + 4 = 0

• 10x – 14y = –4

Answer 1

One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be 10x – 14y = –4.

Explanation:

Given equation of line is –5x + 7y – 2 = 0

Compare with a₁x + b₁y + c₁ = 0

We get a₁ = –5

b₁ = 7

c₁ = –2

Since condition for dependent linear equation is

`a_1/a_2 = b_1/b_2 = c_1/c_2 = 1/k`

∴ `5/a_2 = 7/b_2 = -2/c_2 = 1/k`

⇒ a₂ = –5

b₂ = 7k

c₂ = –2k

Where, k is any arbitrary constant.

Substituting k = 2, then

a₂ = –10

b₂ = 14

And c₂ = –4

∴ The required equation of line becomes – 10x + 14y – 4 = 0

⇒ 10x – 14y + 4 = 0

⇒ 10x – 14y = –4