Equation Systems

TRUE or FALSE:

There are infinitely many solutions to the system of equations.

• TRUE

• FALSE

Fill in the blank for STEP 1:

6x - 2(____) = 24

Solve for x and y

2x − 3y = −1

y = x − 1

• (-2,-3)

• (0,-1)

• (3,4)

• (4,3)

There are 50 donkeys and chickens on a farm.  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

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?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.

• Adult $13
  Child $5

• Adult $10
  Child $6

• Adult $8
  Child $16

• Adult $12
  Child $13

Solve the 3x3 system using the substitution method.

3x + 2y - z = 1

2x + y + z = 8

x + 3y + 4z = 13

• (3,-2,4)

• (3,2,4)

• (1/2,2,2)

• (4,-2,3)

2x+y+3z=11

-4x-y-z=1

x+2y-z=0

• (-2,3,4)

• (3,4,-2)

• (4,-2,3)

• (2,-3,-4)

Solve the 3x3 system using the elimination method.

• (-1,6,-1)

• (3/4,6,1)

• (6,-1,-1)

• (1,6,1)

3x+2y-z=20

2x+y+z=11

x+3y+4z=7

• (5,2,-1)

• (-1,5,2)

• (2,-1,5)

• (1/2,0,2)