If the system of equations $2x + 3y = 10, x+ky= 4$ has a unique solution, then

$k ≠ 3/2$

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