The school that Julia goes to is selling tickets to the annual dance competition. On the first day
of ticket sales the school sold 5 adult tickets and 13 child tickets for a total of $159. The school
took in $51 on the second day by selling 1 adult ticket and 5 child tickets. What is the price each
of one adult ticket and one child ticket?!

We have a system of equations in two variables, namely, a and c. Use the substitution to find a and c.

The price of 1 adult ticket is $11, while the price of one child ticket is $8.

Step-by-step explanation:

Let's identify what we already know:

1) On the first day of ticket sales, the school sold $159 worth of tickets.

2) On the first day, they sold 5 adults tickets, and 13 adult tickets.

3) The school sold $51 worth of tickets on the second day.

4) The school sold 1 adult ticket, and 5 child tickets.

Let's create two formulas:

(5 times x) + (13 times y) = $159

(1 times x) + (5 times y) = $51

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction