I need a little help... just can't figure this question out.

Using gaussian elimination I got (2-b)z = 2 - b.For what values of a and b does the system

ax + bz = 2

ax + by + 4z = 4

ay + 2z = b

have:

- (i) no solution

- (ii) a unique solution

- (iii) a one parameter solution

- (iv) a two parameter solution

Substituting a=0 gives z=1 and b=2 but nothing for x or y so at a guess that would be the 1 parameter solution.

Substituting b=0 gives ax=2, ay+4z=4 and ay+2z = 0. Rearranging and subsituting gives 2z=4 so z=2, and -ay=4. So -ay=2ax which means -y=2x

That is all I could think to do.