Systems of equations all methods

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

Tags

CCSS.HSA.CED.A.3

John and Vicki are training for a 5km race.  John has already run 20 kilometers and plans to run 10 kilometers each day.  Vicki has already run 30 kilometers but plans to run only 5 kilometers per day. The graph below displays each of their training schedules. Which system of equations could be used to determine by which day both John and Vicki will have run the same amount in their training schedule?

• John: y = 20x + 10    Vicki: y = 30x + 5
• John: y = 10x + 20    Vicki: y = 30x + 5
• John: y = -10x + 20  Vicki: y = 5x + 30
• John: y = 10x + 20  Vicki: y = 5x + 30

Tags

CCSS.8.EE.C.8C

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15

Tags

CCSS.HSA.CED.A.3

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:
x + y = 21
6x + 4y = 104

• (10, 11)
• (12, 9)
• (11, 10)
• (9, 12)

Tags

CCSS.8.EE.C.8C

A local fish market is selling fish and lobsters by the pound. The fish costs $5.25 a pound, while the lobster costs $10.50 a pound. The fish market sells 28.5 pounds and makes $215.25?

• The market sold 16 pounds of fish and 12.5 pounds of lobster.
• The market sold 18 pounds of fish and 10.5 pounds of lobster.
• The market sold 12.5 pounds of fish and 16 pounds of lobster.
• The market sold 10.5 pounds of fish and 18 pounds of lobster.

Tags

CCSS.6.NS.B.3

Lisa and Tammy are selling items at the craft show.  Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?

• (1, 12)
• (3, 19)
• (5, 25)
• (0, 10)

Tags

CCSS.8.EE.C.8B

Two numbers have a sum of 25.

One number is five more than the other number.

Find the numbers. Solve using any method.

• The two numbers are 10 and 15.

• The two numbers are 10 and 5.

• The two numbers are 20 and 5.

• The two numbers are 15 and 20.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Angelina spent $16 for a total of 12 pieces of candy, chocolate bars and lollipops. Each chocolate bar costs $2 and each lollipop costs $1.

How many chocolate bars and lollipops did Angelina buy?

• 4 chocolate bars and 8 lollipops

• 8 chocolate bars and 4 lollipops

• 2 chocolate bars and 10 lollipops

• 5 chocolate bars and 7 lollipops

Tags

CCSS.8.EE.C.8C

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.  
Solve: x= apples, y= bananas

• (1.75, 1)
• (1.5, 1.17)
• (-10.7, 9.3)
• (1, 1.5)

Tags

CCSS.8.EE.C.8C

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Tags

CCSS.8.EE.C.8A