I'm doing homework and there is one question that I am suck on, the example in the text does not explain it enough to really get, for me so I figured if someone could go through it and show / explain me the steps, it would be much appreciated.
Anyways the question itself is
In each of the following, find conditions on a and b such that the system has no solution, one solution, and infinitely many solutions
x + by = -1
ax + 2y = 5
The Solution in the book says
If ab =/= 2, unique solution x = (-2-5b)/(2-ab) y= (a+5)/(2-ab)
If ab=2: no solution if a =/= -5 ; if a = -5, the solutions are x=-1+2/5t, y=t.
Could someone please go through this problem explaining how I find this answer?