Originally Posted by

**dems** Hi guys, I was hoping someone could walk me through how to find conditions on 'a' and 'b' such that the system has i) no solution ii) one solution and iii) infinite solutions.

x - 2y = 1

ax + by = 5

The solutions are provided below but I really have no idea how I am supposed to arrive at these conclusions.

Thanks for your time and help!

__Solutions__

i) If b 6=/= 2a, unique solution x = (b+10)/(b+2a) , y = (5-a)/(b+2a)

ii) If b = -2a : no solution if a =/= 5;

iii) If a = 5 the solutions are x = 1 + 2t, y = t