[SOLVED] System of Linear Equations

I have another question regarding another problem. The system is:

x + y = 0

y + z = 0

x + z = 0

ax + by + cz = 0

Find values for a, b, and c so that the system has:

(a) a unique solution

(b) no solution

(c) an infinite number of solutions

I know for a fact it is not possible for this system to have no solution. It has the trivial solution x = y = z = 0. Also, it seems if a + b + c != 0, then it may have an infinite number of solutions. To be honest aside from already knowing part b, I am not quite certain how to proceed. Thanks again for help!