What's the solution of this equation?

Pls! does anybody know a shortcut for answering these types of questions in the future?

At the county fair, the baxter family bought 6 hot dogs and 4 juice drinks for $12.90. the farley family bought 3 hot dogs and 4 juice drinks for $8.55. find the price of a hot dog and the price of a juice drink.

Select the conic section that represents the equation. 3x2 + 3y2 -2x + 4 = 0