Question

The value of k for which the pair of linear equations kx- y = 2 and 6x-2y = 3 has a unique solution, is

• A. k=3
• B. K≠3
• C. K=0
• D. K≠0

Answer 1

The Correct Option is B

The system of linear equations will have a unique solution if the determinant of the coefficient matrix is non-zero. The given system is: \[ kx - y = 2 \quad \text{(1)} \quad \text{and} \quad 6x - 2y = 3 \quad \text{(2)}. \] The coefficient matrix is: \[ \begin{pmatrix} k & -1 \\ 6 & -2 \end{pmatrix}. \] The determinant of this matrix is: \[ \text{Determinant} = k(-2) - 6(-1) = -2k + 6 = 6 - 2k. \] For a unique solution, the determinant must not be zero: \[ 6 - 2k \neq 0. \] Solving for \( k \): \[ 6 \neq 2k \quad \Rightarrow \quad k \neq 3. \] Thus, the value of \( k \) must not be 3 for the system to have a unique solution.

The correct option is (B): \(K≠3\)