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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.


$x+y≥100\\\ 10x+5y≥900$


$x=100\\\ 10x+5y\le 900$


$x+y\le 100\\\ 10x+5y\le 900$


$x+y=100\\\ 10x+5y=900$

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