Systems of Equations Word Problems

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91
• x + y = 91
  14.80x + 17y = 6
• x + y = 6
  14.80y + 17x = 91
• x + y = 91
  14.80x+ 17y = 6

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?

• 4x + 7y = 578
  x + y = 3365
• 4x + 7y = 3365
  x + y = 578
• 4y + 7x = 578
  x + y = 3365
• 4y + 7x = 3365
  x + y = 578

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.

• x + y = 21
  6x + 4y = 104
• x + y = 104
  6x + 4y = 21
• x + y = 21
  6y + 4x = 104
• x + y = 104
  6x + 4y = 21

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104

• A= 10 
  C=11
• A = 12
  C = 9
• A= 11
  C = 10
• A= 9
  C= 10

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

What is the solution to this system of linear equations? 
Use substitution.

y = -2x - 6
-2x + y = 6

• (0, -3)
• (-3, -12)
• (-3, 0)
• (3, -12)

What is the solution to this system of linear equations?
Use elimination.

2x + y = 17
   x + y = 10

• (7, 5)
• (9, -1)
• (-1, 9)
• (7, 3)

Solve the following system by graphing.  What is the solution?

• Infinite number of solutions
• (3, 3)
• (3, -3)
• (-3, 3)