Systems of Equations in Two and Three Variables

Give the solution to the system.

• (3,1)

• (1,3)

• (-1,3)

• (1, -3)

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

• 3H + 2D = 315

  2H + 4D = 450

• 3H + 2D = 450

  2H + 4D = 315

• 2H + 4D = 315

  3H + 2D = 450

• 3H + 2D = 315

  2H + 2D = 135

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?

• 1.5N+0.5S=78.5

  N+S=87

• 1.5N+0.5S=78.5

  1.5N+0.5S=87

• N+S=78.5

  1.5N+0.5S=87

• N+S=78.5

  N+S=87

There are 50 donkeys and chickens on a far.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174
  4d + 2c = 50

• d + c = 50
  4d + 2c = 174

• d + c = 50
  2d + 4c = 174

• d + c = 174
  2d + 4c = 50

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child ticket

• 3S+C=38

  3S+2C=52

• 3S+C=52

  3S+2C=38

• 3C+S=38

  3C+2S=52

• 3C+S=52

  3C+2S=38

What kind of system is represented by the three planes?

• Consistent and Independent

• Consistent and Dependent

• Inconsistent

What is the solution set of the given system?

• (1,-1, 0)

• The system has no solution.

• (13/4, 1/4, 31/4)

• 2x+2z=7 and x+z=11 

• 2x+2z=7 and x+z=5

• 2x+2z=7 and x-z=11 

What is the weight of Box Y?

• 2 kg

• 4 kg

• 6 kg

• 9 kg