PLEASE ANSWERRR! FIRST CORRECT ANSWER WILL VOTE BRAINLIEST For a certain value of k, the system
x + y + (k-1) = 2,
6x + 2y - 3z = 1
kx - z = -3
has no solutions. What is this value of k?

In matrix form, the given system is written as

and the system has no solution is the coefficient matrix is singular. The determinant is

and this is zero when k = 4/3.

On the other hand, in case you are missing a factor of z in the first equation, so that the system should read

x + y + (k - 1) z = 2

6x + 2y - 3z = 1

kx - z = -3

reframing it as a matrix equation gives

Then the determinant of the coefficient matrix is

and the determinant is zero at two values, k = (-1 ± √33)/4.