Systems Elimination and Word Problems

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

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

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5 
  Oatmeal Cookies $3
• Sugar Cookies $4
  Oatmeal Cookies $8
• Sugar Cookies $2
  Oatmeal Cookies $6
• Sugar Cookies $3
  Oatmeal Cookies $6

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.  How many nickels and dimes did Dennis earn? 

• 40 nickels, 40 dimes
• 52 nickels, 28 dimes
• 28 nickels, 52 dimes
• 30 nickels, 50 dimes

Solve the system by elimination.
14x - 9y = 1
-7x + 3y = 16

• (10, -11)
• (-10, 11)
• (-11, 11)
• (-7, -11)

Solve by elimination.

6x - y = 2

-3x - 6y = 12

• (2,0)

• no solution

• (0,-2)

• infinite solutions

Solve by elimination
-12x-4y= -8 
  -6x-2y= -4

• no solution 
• (0,0)
• infinite solutions 
• (4,0)

What would be the first step in finding the solution using elimination?

2x + 2y = -2

3x - 2y = 12

• you cannot solve this using eliminiation

• cross out the 2x and 3x

• cross out the 2y and -2y

• change to slope intercept form and graph

7x - y = 10

-7x + y = -14

• No Solution

• (4, 1)

• Infinitely Many Solutions

• (2, -4)

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:

• (10, 11)

  10 adults 11 children

• (12, 9)

  12 adults 9 children

• (11, 10)

  11 adults 10 children

• (9, 12)

  9 adults 12 children