Question

For what values of $k$, the system of equations $x-2y=3,3x+ky=1$ has a unique solution?

Answer 1

$x-2y=3$

$3x+ky=1$

$3(3+2y)+ky=1$

$9+6y+ky=1$

$y(6+k)=-8$

$y=\frac{-8}{6+k}$

for $k\ne -6$ it have a unique

$so{l}^n$

&

for $k=6$ no $so{l}^n$