Me usó

Me usó
 

Hi,

From Duolingo:

¡Me usó la tarjeta para comprar un equipo de música!

accepted translation:

He used my card to buy a sound system!

The card was mine, not his. Does it follow from the context, or is it determined grammatically?

He could have used his card to buy me a sound system, after all :D

Colloquial usage of the indirect object pronouns. It underlines that a person did something that affected another, from the point of view of the offended. :)
It's more commonly used with "me", because it's mostly my ego the one that's hurt by someone else's actions. "They did this to me!" ;)

Your sentence has the same meaning as: "Usó mi tarjeta de crédito para comprar(se) un aparato de sonido". ("Un equipo de música" is the same object, but in Mexico "aparato de sonido" is more common.) :)
He used my money to buy something without my knowledge, so this is felt like he did this to me on purpose to hurt me.

Some more examples:
- Los niños no me comen bien. -> Obviously, the children won't eat their mother, but rather they refuse to eat the food she offers them.
- Mi hijo se me casa el viernes. -> The son is getting married and the parent is sad about it.
- El perro me destruyó todas las almohadas de la casa. -> The dog destroyed the pillows, with or without an intention to be obnoxious, but I felt it as a personal offense.
- Nuestros bebés se nos fueron de la casa. -> Parents talking about their children leaving their home, obviously hurt by their action, even if it's not meant that way. :)