Question

Write the number of solutions of the following pair of linear equations:

x + 3y – 4 = 0, 2x + 6y – 7 = 0

Answer 1

The given pair of linear equations are

x + 3y – 4 = 0   ...(i)

2x + 6y – 7 = 0   ...(ii)

Which is of the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, where

a₁ = 1, b₁ = 3, c₁ = –4, a₂ = 2, b₂ = 6 and c₂ = –7

Now

`(a_1)/(a_2) = 1/2`

`(b_1)/(b_2) = 3/6 = 1/2`

`(c_1)/(c_2) = (-4)/(-7) = 4/7`

⇒ `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`

Thus, the pair of the given linear equations has no solution.