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

Solution:

GIVEN: 

$k x+2 y=5$

 

$3 x+y=1$

To find: To determine to value of k for which the system has a unique solution.

We know that the system of equations

$a_{1} x+b_{1} y=c_{1}$

 

$a_{2} x+b_{2} y=c_{2}$

For unique solution

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Here,

$\frac{k}{3} \neq \frac{2}{1}$

$k \neq 6$

Hence for $k \neq 6$ the system of equation has unique solution.