I'm just trying to figure out how to get this to rref:

x + 5y + z = 0

x + 6y - z = 0

2x + ay + bz = c

1 5 1 0

1 6 -1 0

2 a b c

I know the following is the answer, but I'm now sure how to get there. The problem I'm having is that I don't know how to handle the a, b and c. I probably just need someone to explain how to do the bottom row.

1 0 0 -11c/(2a+b-22)

0 1 0 2c/(2a+b-22)

0 0 1 c/(2a+b-22)

Thanks