System of Linear Equations: a & b Values

[Unslain]

Homework Statement

For the following system, indicate for what values of a and b the system will have
i.) One Solution
ii.) No Solutions
iii.) Infinitely Many Solutions

Homework Equations

2x + y - az = 1
5x + 3y - 2az = 2+2b
x + y + az = b

The Attempt at a Solution

[ 1 0 -2a | 1-b ]
[ 0 1 2a | 3b-1 ]
[ 0 0 a | -b ]

Every time I row reduce the system I end up with a row echelon form that leaves me with no means to decipher a and b. Making me think I'm doing something wrong.

Thanks.

 

[Dick]

I think you'll need to show use what you got for the row echelon reduction before anyone can comment.

 

[Unslain]

Yeah I just put it in the original post.

Thank you for the heads up.