2) The school that Gabriella goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 4 adult tickets and 4 child tickets for a total of \( \$ 76 \). The school took in \( \$ 94 \) on the second day by selling 6 adult tickets and 1 child tickets. Write a system of equations for this situation. Solve the system for extra credit.

Let \( x \) represent the price of an adult ticket and \( y \) the price of a child ticket. Based on the ticket sales, we can set up the following system of equations: 1. From the first day’s sales: \( 4x + 4y = 76 \) 2. From the second day’s sales: \( 6x + 1y = 94 \) Now, let's simplify and solve the system. 1. From the first equation, divide everything by 4: \( x + y = 19 \) (Equation 1) 2. The second equation remains: \( 6x + y = 94 \) (Equation 2) Next, we can substitute \( y = 19 - x \) from Equation 1 into Equation 2: \( 6x + (19 - x) = 94 \) Combine like terms: \( 5x + 19 = 94 \) Subtract 19 from both sides: \( 5x = 75 \) Dividing by 5 gives: \( x = 15 \) Now substituting \( x = 15 \) back into Equation 1: \( 15 + y = 19 \) Thus, \( y = 4 \) So the price of an adult ticket is \( \$15 \) and the price of a child ticket is \( \$4 \).