Question

How many solutions does the system formed by x-y=3 and ay-ax+3a=0 have for a nonzero number a? Explain.

Answer 1

There's no solution that is nonzero.
x-y=3
x = 3+y

Substitute that to the second equation.
ay-a(3+y)+3a=0
6a=0
a=0

y = x-3

Substitute that to the second equation
a(x-3)-ax+3a=0
0 = 0