Question 381398
Let x be the price of an adult ticket and y be the price of a youth ticket. We have

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

Adding the two equations and dividing by 5, we obtain

x + y = 56

Since 2x + 3y = 2(x + y) + y = 2(56) + y = 112 + y we can substitute into the first equation to get

112 + y = 134 --> y = 22

Therefore the price of a youth ticket is $22.