There are three unknowns to be found. We need to find one that can set up the equations easily.
There are 3 more dogs than cats.
There are 6 fewer birds than cats.
We see that cats (C) would be a useful variable because everything else is related to it.
C+3= number of dogs
C = number of cats
C-6 = number of birds
Add them all up, we have
3C+3-6=90
Add 3 to each side,
3C=93
C=31 .............. There are 31 cats
C+3=34...............There are 34 dogs
C-6=25 .............. There are 25 birds..........Total 90 pets.