Answer :
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.
[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.
