Question

Find the value of k for which the system:
kx + 2y = 5, 3x + y = 1 has a unique solution

• A. $k=6$
• B. $k\ne 9$
• C. $k\ne 6$
• D. $k=6$
• E. None of these

Answer 1

The correct option is C $k\ne 6$

We have, kx + 2y = 5 ...... (1)
3x + y = 1 ...... (2)
Here, $a_1=k,b_1=2,c_1=5$
$a_2=3,b_2=1,c_2=1$
The given system of equations will have a unique solution
if $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$ i.e., if, $\frac{k}{3}\ne \frac{2}{1}$
i.e., if $\frac{k}{3}\ne 2$ i.e., if $k\ne 6$