Linear Equations by Elimination

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

• (1, -10)

• No solution

• (-4, 1)

• (1, 10)

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

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

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x
  y = 8.40 + x

• y = 9.65x + 43
  y = 8.40x + 58

• y =9.65x
  y = 8.40x

• y = 9.65x - 43
  y = 8.40x - 58

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

Solve by elimination:
7x-9y=29

7x+2y=-15

• (-4,-1)

• (-1.-4)

• (-1,4)

• (-1,6)

Solve by elimination:
7x+y=-9

-3x-y=5

• No solution

• (1,8)

• (-2,-3)

• (-1,-2)

Solve the system using any method. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• No solutions

• (6, 4) 

Solve the system of linear equations by elimination.

• (4, 3)

• (-2, 1)

• (3, 0)

• (3, 6)

• (4, -1)

• (2, 1)

• (-1, 3)

• (1, -3)