If the system of 3 equations

ax+b+z=0

x+by+z=0

x+y+cz=0

has a non-trivial solution, then 1/(1-a) + 1/(1-b) + 1/(1-c) = ?

The choices are 1, 2, 0 or -1

It seems obvious to me that if a=b=c=1, the system reduces to one equation and has a non-trivial solution. But infinity isn't among the options.

Oh, and there isnt any clause stating that a, b and c are distinct.