So my linear algebra class is just starting.

So while I realize this isn't a linear algebra thread, it's in a realm of difficultly similar to that of Pre-Calculus

What are the value(s) of α such that the system has:

a) no solution

b) a unique solution

c) infinite number of solutions

*Solve case c ( with many solutions) parametrically

x + y = 1

αx + 2y = 2

For case b, I'm getting that α can be anything EXCEPT 2. Thus x would be equal to 0, and y equal to 1.

For case c, the only solution I can seem to come up with is α=2.

I'm not sure there is any solution to case a, and I'm unsure of case b and c.

Normally I wouldn't be stuck on a question of system of equations, but this really has me stuck.