Question

How many soulutions doses the system formed by x-y=3 and ax+3a=0 have for a nonzero number a

Answer 1

We have that
x-y=3 -------> equation 1
and
ax+3a=0------> equation 2

we know that

ax+3a=0-------> a*(x+3)=0
a=0    and (x+3)=0
if a is a nonzero number
then 
only
x+3=0------> x=-3

substitute the value of x=-3 in the equation 1
x-y=3------> (-3)-y=3-----> y=-6

the system has one solution-------> the point (-3,-6)