Variables:
a: 1 adult ticket cost
c: 1 child ticket cost
2 adults and 3 children cost $28, that is,
2a + 3c = 28 (eq. 1)
1 adult and 2 children cost $22, that is,
a + 2c = 22 (eq. 2)
Isolating a from equation 2:
a = 22 - 2c
Substituting this equation into equation 1:
2(22 - 2c) + 3c = 28
2*22 - 2*2c + 3c = 28
44 - 4c + 3c = 28
44 - c = 28
44 - 28 = c
16 = c
Replacing this result into the third equation:
a = 22 - 2*16
a = 22 - 32
a = -10
(I think there is a mistake in the question, a ticket cannot cost -$10)
