Question

Find the value of k for which the following system of equations has a unique solution:

kx + 2y = 5

3x + y = 1

Answer 1

Given: kx + 2y = 5, 3x + y = 1

Form the coefficient matrix and its determinant:

D = `|(k, 2), (3, 1)|` 

= k × 1 – 2 × 3 

= k – 6

A 2 × 2 linear system has a unique solution if its determinant ≠ 0, so k – 6 ≠ 0 ⇒ k ≠ 6.

The system has a unique solution for all real k except k = 6.