The families vistes the local fair over a holiday weekend: - the Rawlins family spent $51 on admission for 2 children and 3 adults, plus 50 carnival tickets
- the alverez family spent $90 on admission for 4 children and 6 adults, plus 100 carnival tickets
- The talbot family spent $78 on admission for 2 children and 5 adults, plus 80 carnival tickets

Which matrix equation can be solved to find the cost of admission for children, x, the cost of admission for adults, y, the cost of each carnival ticket, z?