Systems Elimination and Word Problems

When applying the elimination method to the system of equations 5x - 2y = 10 and 10x + 2y = 40, what is the resulting equation after the first step?

• 15x = 50

• 5x = 15

• 15x + 4y = 50

• 10x = 30

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.

8x + 9y =  -24

-8x − y = 16

• 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.

4x + 9y =  1

4x − 7y = 11

• 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

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

-8x + 6y =  12

-8x − 7y = 1

• 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) 

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49

• x + y = 49
  10x + 5y = 1430 

• x + y = 49
  20x + 50y = 1430

• x + y = 49
  x + y = 1430

what do you need to multiply the top equation by to make a zero pair:

5x - 2y = 11

-10x + 3y = -4

• 5

• -1

• 2

• -2