One family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park. another family spends $146 on 3 adult tickets and 2 youth tickets at the same amusement park. what is the price of a youth ticket?
so this is elimination and i'm starting to get the hang of it; so you basically just find out x(let's just say that youth tickets)?

3x + 2y = $134
2x + 3y = $146

Using elimination to solve for x

9x +6y = 3*134 Multiplying 1st equation by 3

-4x -6y = -2*146 | Multiplying 2nd equation by -2

5x = 3*134 - 2*146

5x = $110

x = $22, the cost of the youth ticket

Put x= 22 Into An Equation Then Solve For y

3(22)+2y= 134
66+ 2y=134
Subtract 66
2y=68
Y= 34

CHECKING Answer ($34 being the cost of the adult ticket) y = (134-3*22)/2

3*$22 + 2*$34 = $66 + $68 = $134