Systems of Equations in Context

Erica works in a soda-bottling factory.  As bottles pass her on a conveyer belt, she puts caps on them.  Unfortunately, Erica sometimes breaks a bottle before she can cap it.  She gets paid 4 cents for each bottle she successfully caps, but her boss deducts 2 cents from her pay for each bottle she breaks.

Erica is having a bad morning.  Fifteen bottles have come her way, but she has been breaking some and has only earned 6 cents so far today. 

Which system of equations would help you determine how many bottles Erica capped and how many she broke?

1. 
   

• 1. Let c = the number of capped bottles and b = the number of broken bottles

  2. c + b = 15

  3. 4c − 2b = 6

• 1. Let c = the number of capped bottles and b = the number of broken bottles

  2. 6c + 6b = 15

  3. 4c − 2b = 6

• 1. Let c = the number of capped bottles and b = the number of broken bottles

  2. c + b = 6

  3. 4c − 2b = 15

• 1. Let c = the number of capped bottles and b = the number of broken bottles

  2. 4c − 2b = 15

Erica works in a soda-bottling factory.  As bottles pass her on a conveyer belt, she puts caps on them.  Unfortunately, Erica sometimes breaks a bottle before she can cap it.  She gets paid 4 cents for each bottle she successfully caps, but her boss deducts 2 cents from her pay for each bottle she breaks.

Erica is having a bad morning.  Fifteen bottles have come her way, but she has been breaking some and has only earned 6 cents so far today.  How many bottles has Erica capped and how many has she broken?

• Erica capped 15 bottles

• Erica capped 6 bottles

• Erica broke 2 bottles

• Erica broke 9 bottles

The elimination method would work best for the following system of equations:

x = 4 - 2y

3x - 2y = 4

• True
• False

Which method (Substitution or Elimination) would best help you solve the following system of equations?

x = -5y + 2

x = 3y - 2

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Solve the following system of equations with whichever method you prefer:

y = 1/2x + 4

y = -2x + 9

What should be your first step to solve the following system of equations using the Elimination Method?

5x + 3y = -6

2x - 9y = 18

• Add the equations together to eliminate the x's

• Multiply the top equation by 3, so you can eliminate the y's

• Multiply the bottom equation by 2, so you can eliminate the x's

• Set the two equations equal to each other

Solve the system of equations:

3x + y = 1

4x + y = 2

• x = 1

• y = 4

• y = -2

• x = 0

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

The following system of equations have infinite solutions.

2x - 4y = 10

x = 2y + 5

• True
• False

What is a solution to a system of equations?

• Where the two lines intersect

• The location where either lines crosses the x-axis

• The location where either lines crosses the y-axis

• The difference between the slopes of the two lines

Tags

CCSS.8.EE.C.8