The given system of equations is:
kx + 2y – 5 = 0
3x + y – 1 = 0
The above equations are of the form
a1x + b1y − c1 = 0
a2x + b2y − 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
\(\frac{a_1}{a_2} ≠ \frac{b_1}{b_2}\)
\(\frac{k}{3} ≠ \frac{2}{1}\)
⇒ k ≠ 6
Hence, the given system of equations will have unique solution for all real values of k other than 6.
