Elimination Systems Problems

Solve the following system by using elimination:

-2x - 5y = -15

x + 8y = 13

• (5, 1)

• (1, 5)

• (5, -1)

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6

• x + y = 4
  x - y = 6

• 4x + 6y = 13
  3x + 7y = 13.5

• 4x - 6y = 13
  3x - 7y = 13.5

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530

What do you get for y when you start solving

• 2

• -1

• 1

• -2

Which variable would be the BEST choice to try and eliminate?

• x

• y

What does the new equation become after multiplying?

• -12x + 6y = 26

• -12x + 18y = 26

• -12x + 18y = 78

When using the elimination method to solve the system of equations 4x + 3y = 20 and 2x - 3y = 10, what is the resulting equation after the first step?

• 3x + 3y = 30

• 2x = 20

• 6x = 30

• 5x = 25

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

8x + 9y =  −82

-x − 9y = 89

• Add to eliminate x

• Add to eliminate y

• Subtract to eliminate x

• Subtract to eliminate y

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

3x + 7y =  14

4x − 7y = 21

• Add to eliminate x

• Add to eliminate y

• Subtract to eliminate x

• Subtract to eliminate y

Solve the system by elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4)