If the system of equations $2x + 3y = 10, x+ky= 4$ has a unique solution, then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $k ≠ 3/2$
Given system of equations:
2x + 3y = 10
x + ky = 4
For a unique solution, the determinant of the coefficient matrix must be non-zero:
Coefficient matrix:
$\begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix}$
Determinant: Δ = (2)(k) − (3)(1) = 2k − 3
For unique solution: Δ ≠ 0
2k − 3 ≠ 0
2k ≠ 3
k ≠ 3/2
Therefore, the system has a unique solution if k ≠ 3/2