what a will give us:
1. One Solution
2. No solution at all.
3. Infinite Solutions
If any one of those equations is impossible there will be no solution. In particular, the last equation can be written (1+ a)(2z+ w)= 3. What happens if a= -1?
For other values of a, you have three equations in four unknown variables. There is NO value of a such that this has a unique solution.