Hillary plans to go on 3 rides and play 6 games at the state fair, which will require a total of 42 tickets. James will play 5 games and go on 4 rides. He needs 44 tickets. Determine the system of equations that can be used to find the number of tickets it takes to go on one ride, r, and the number of tickets it takes to play one game,

g. Assume all rides require the same number of tickets, and all games require the same number of tickets. 3

Let x be the number of tickets required to go on a ride and y be the number of tickets required to play a game. Our system of equations will therefore be:

3x + 6y = 42

4x + 5y = 44

Lets use elmination to solve the system. First lets multiply the first equation by 4 and the second equation by 3.

12x + 24y = 168

12x + 15y = 132

Now we can subtract one equation from the other to eliminate the x terms.

12x + 24y = 168

- (12x + 15y = 132)

0 + 9y = 36

9y = 36

y = 4

Now that we've solved for y, we can plug this value into one of the equations and solve for the unknown x.

4x + 5 (4) = 44

4x + 20 = 44

4x = 24

x = 6

Thus, it takes 6 tickets to get on a ride and 4 tickets to play a game.

Hillary: 3r + 6g=42

James: 4r + 5g = 44