Solving systems of equations?

[Mongaa]

Hey guys I just needed some help with this question:

Consider the following system of simultaneous equations.

6x+2y-z=1
x+y+z=2
kx+y-z=1

For what values of k, is there:
i.) a unique solution?
ii.) no solution?

I've tried it multiple times but can't seem to get it.
Thanks 

[achre]

This is tech active, right? Would it be as simple as plugging the matrix of coefficients into your calculator, storing it as a, and solving det(a)=0 for k? [solve(det(a)=0,k)]
Which spits out k=11/3 as the only solution.
So you'd have a unique solution when k ∈ R\{11/3} and no solution when k=11/3.
If that's wrong, let me know.

[Daenerys Targaryen]

You can also do it simultaneously (algebraically)
I named them [1], [2], and [3]
I transposed [2] to call this [4]

In [1], sub in [4]

[5]



In 3, sub in [4]

[6]




In [5] and [6]

For unique solution;









Thus for unique solution k ∈ R\{11/3}