When solving system's of equation what does t represent in this problem and when/why does it occur?

Question

4 x - y + z = 5

2 y + 6 z = 3 0

x + z = 5

I had set up a matrices based on the equations above and formed:

4  -1  1   5

0  2   6   30 

0  0   8   0

In the question it stated:

Solve the system if possible. (If a free variable is needed use the parameter t. If the system is inconsistent, enter INCONSISTENT.) When searching up how to answer this problem, i was left confused since their was a variable called t I left out according to the question so how do i approach these types of problems in general.

~ Thankyou if you can explain how to do these problems in full anywho.