Answer:
 small dogs
 small dogs
Step-by-step explanation:
Let  be the number of large dogs and
 be the number of large dogs and  be the number of small dogs.
 be the number of small dogs.
Since it is given that the toal number of dogs that signed up is 49, this makes our first equation  .
.
Also, there are 36 more small dogs than large dogs that signed up to compete, so this makes our second equation  .
.
Since the value of  is already solved in our second equation, we can plug it into the first equation and solve for
 is already solved in our second equation, we can plug it into the first equation and solve for  :
:







Now plug the value of  into either equation and solve for
 into either equation and solve for  :
:




Even though the answer isn't realistic, it's still correct.