The Copper Town Animal Shelter houses stray dogs and cats. It has room for up to $100$ animals in all. It also has budget restrictions on how much pet food it can purchase per week. The shelter can spend no more than $\$900$ on food for all of the animals. It costs the shelter $\$10$ a week to feed each dog and $\$5$ a week to feed each cat.
Letting $x=$ number of dogs and $y=$ number of cats, write a system of inequalities that represents the information in the paragraph above.