The definition of "economics" is:
the branch of knowledge concerned with the production, consumption, and transfer of wealth.
While for "economy" it is:
the state of a country or region in terms of the production and consumption of goods and services and the supply of money.
"economics" is usually a term used for education, such as a major or subject in school, it means the learning process and knowledge of "production, consumption, and transfer of wealth.".
Example sentence with "economics":
She majored in economics
He gained a first class Honours degree in economics.
He is regarded as a committed supporter of a radical free-market economics policy.
However, "economy" is different, it means the state of a country/city in terms of the supply of money. You usually use it with:
The war altered the country's economy
An increase in tourism will help the city's economy
The economy was affected by the establishment of a land tax.