# Math Help - linear system

1. ## linear system

x + 2y + 3z = a
2x +5y + 3z = b
x + 8z = c

what is condition should a,b,c be so that this system:
a) have exact one solution
b) have no solution
c) have infinit number of solution

please explain it step by step
i really need it.
thanks

2. The determinant of the system is equal to -1, so the system has only one solution, $\forall a,b,c$

3. i dont quite get what you mean, can you make it a little clearer ? thx