Solve both equations for y:
[tex]x-y=3 \ \ \ |-x \\
-y=-x+3 \ \ \ |\times (-1) \\
y=x-3 \\ \\
ay+3a=0 \ \ \ |-3a \\
ay=-3a \ \ \ |\div a, a \not= 0 \\
y=-3[/tex]
Set the expressions equal to each other:
[tex]y=y \\ x-3=-3 \ \ \ |+3 \\
x=0 \\ \\
(x,y)=(0,-3)[/tex]
So, for every nonzero number a the system of equations has one solution.
