Find the value of k for which each of the following system of equations have no solution :

GIVEN:

$2 x-k y+3=0$

$3 x+2 y-1=0$

To find: To determine for what value of k the system of equation has no 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 no solution

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

Here,

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

$\frac{2}{3}=\frac{-k}{2}$

$k=\frac{-4}{3}$

Hence for $k=\frac{-4}{3}$ the system of equation has no solution.