Question

For the pair of equations λx + 3y = –7, 2x + 6y = 14 to have infinitely many solutions, the value of λ should be 1. Is the statement true? Give reasons. 

Answer 1

No, the given pair of linear equations

λx + 3y + 7 = 0 and 2x + 6y – 14 = 0

Here, a₁ = λ, b₁ = 3, c₁ =7,

a₂ = 2, b₂ = 6, c₂ = –14

If `a_1/a_2 = b_1/b_2 = c_1/c_2`, then system has infinitely many solutions.

⇒ `λ/2 = 3/6 = - 7/14`

∵ `λ/2 = 3/6`

⇒ λ = 1

And `λ/2 = - 7/14`

⇒ λ = –1

Hence, λ = –1 does not have a unique value.

So, for no value of λ the given pair of linear equations has infinitely many solutions.