Solve the following system, where a, b, and c are constants:

x1 + x2 + x3 = a

2x1 + 2x3 = b

3x2 + 3x3 = c

If I put this into a matrix I get:

1 1 1 | a

2 0 2 | b

0 3 3 | c

I'm really not sure where to go from here because it seems to me like row 2 and 3 will cancel out making b and c equal 0, but I'm not really experienced with this and I'm not even sure what I'm trying to obtain in the end.

Thanks