Question

For the pair of equations λx + 3y + 7 = 0 and 2x + 6y - 14 = 0. 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, Comparing with ax + by + c = 0;

Here, a₁ = λ, b₁ = 3, c₁ = 7;

And a₂ = 2, b₂ = 6, c₂ = - 14;

a₁ /a₂ = λ /2

b₁ /b₂ = 1/2

c₁ /c₂ = - 1/2

If a₁/a₂ = b₁/b₂ = c₁/c₂, then system has infinitely many solutions.

So λ /2 = 1/2

λ = 1

Also λ /2 = - 1/2

λ = -1

Since,λ does not have a unique value.

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