Solving Systems of Linear Equations by Elimination

Solve the system by elimination.
  5x + 8y = -12
3x + 5y = -7

• (1, -10)

• No solution

• (-4, 1)

• (1, 10)

Solve by elimination
-12x-10y= 0
6x+5y= -1

• infinite solutions

• (0,0)

• no solution

• (2,1)

Solve using elimination. 
−4x − 4y = 0
  8x + 8y = 0 

• (−6, −4) 

• Infinite number of solutions  

• No solutions

• (6, 4) 

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

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos
  m: # of glasses of milk

• t: Cost of each taco
  m: Cost of each glass of milk

• t: total cost
  m: # of food items

• t: Cost of each glass of milk
  m: Cost of each taco

8x + 14y = 4

-6x - 7y = -10

• (4, -2)

• (-2, 4)

• (0, 3)

• (-4, -2)

Ride and Transport are two new ride sharing companies in Colorado. Ride is charging $2 for pick up fees and then $2.50 per mile. Transport is charging only $2.70 per mile. How many miles will it take for both companies to charge the same amount? Write a system of equations to solve.

• 27 miles

• 10 miles

• 270 miles

• 100 miles

Your friend rents 10 chairs and 2 tables for $300. Another friend rents 8 chairs and 4 tables for $360. How much does a chair and a table cost? Write a system of equations to solve.

• Chairs $2 Tables $5

• Chairs $50 Tables $20

• Chairs $10 Tables $15

• Chairs $20 Tables $50