I hope I am not bugging you all to much

I have another problem that I can't for the life of me solve. I really hate math and doing math online is the absolute pits. :( I have never been so stressed in all my life.

Thanks again for any help you can give.

The augmented matrix of a system of three equations in the three unknowns x, y, and z is reduced to

[2 1 1 | 1]

[0 3 2 | 4]

[0 0 0 | 0]

Find the solution of the system.

I was thinking z = 0 but the answer in the book is z = k k any integer.

The answers are

x = k + 1/6

y = 4 - 2k/3

z = k k any integer

HOW????

Did I mention I cannot stand math specially online math????