x+5y - 6z = 2
kx +y -z = 3
5x -ky +3z =7
For what values of k does the system have a unique solution
The determinant
|1 5 -6|
|k 1 -1|
|5 -k 3|
must be non-zero.
Turn that into an inequality for k.
(3 -k) +(-25 -15k)+(-6k^2 +30) NOT = 0