Question

Find the value of $k$ for which the equations $kx+2y=5$, $3x+y=1$ has a unique solution.

• A. 6

Answer 1

The correct option is A 6

The given system of equations is:

$kx+2y–5=0$

$3x+y–1=0$

The above equations are of the form

a₁ x + b₁ y − c₁ = 0

a₂ x + b₂ y − c₂ = 0

Here, a₁ = k, b₁ = 2, c₁ = −5

a₂ = 3, b₂ = 1, c₂ = -1

So according to the question,

For unique solution, the condition is

a₁ / a₂ ≠ b₁ / b₂

$k/3\ne 2/1$

⇒ $k\ne 6$

Hence, the given system of equations will have unique solution for all real values of $k$ other than $6$.