Let x be the number of adults that went to the game, and y be the number of children, since the number of total of people that went to the game is 166, then:

Now, each adult ticket had a cost of $2.10, each child's ticket had a cost of $0.75, and the total amount taken in was $293.25. Therefore:

Solving the first equation for x we get:

Substituting the above equation in the second equation and solving for y we get:

Substituting y=41 in the third equation on the board we get:

Answer:
The system of equations is:

Where x is the number of adults that went to the game and y is the number of children.
The number of adults that attended is 125 and the number of children is 41.