Solving System of Equations Applications

A movie theater sells adult tickets for $10 each and child tickets for $6 each. If a total of 100 tickets were sold for $800, write a system of equations to represent this scenario and solve for the number of adult and child tickets sold.

• The number of adult tickets sold is 60, and the number of child tickets sold is 40.

• The number of adult tickets sold is 80, and the number of child tickets sold is 20.

• The number of adult tickets sold is 50, and the number of child tickets sold is 50.

• The number of adult tickets sold is 70, and the number of child tickets sold is 30.

Graph the system of equations: x + y = 5 and 2x - y = 3. Identify the point of intersection.

• (1, 4)

• (2, 3)

• (4, 1)

• (3, 2)

Solve the system of equations by substitution method: 3x - 2y = 7 and 5x + 4y = 11.

• x = 3, y = -2

• x = 2, y = 3

• x = 5, y = 2

• x = -1, y = 4

Graph the system of equations: 2x + y = 4 and x - y = 1. Identify the point of intersection.

• (1, 4)

• (3, 2)

• (5, 1)

• (2, 3)

Find the solution(s) to the system.

• (0,-3)(-1,-2)

• (0,-3)

• (-2,0)(2,0)

• No solution

Find the exact real solutions to the system

• no real solutions

• (0, 5)

• (-10, 11)

• (5, 0)

Solve the system of equations by substitution method: 4x - 3y = 10 and 2x + y = 5.

• x = 2, y = 1

• x = 5, y = 3

• x = 1, y = 4

• x = 3, y = 2

Identify the number of solutions for the system of equations: 2x + 3y = 8 and 4x + 6y = 16.

• Infinite solutions

• No solution

• One solution

• Two solutions

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined.
Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87

• 1.5x+0.5y=78.5
  1.5x+0.5y=87

• x+y=78.5
  1.5x+0.5y=87

• x+y=78.5
  x+y=87

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions