Creating Systems of Linear Equations from Context

A tub has 40 gallons of water in it and starts draining at a rate of 6 gallons per minute. Write a formula for the amount of water left in the tub.

• y = 6x + 40

• y = -6x + 40

• y = 6x - 40

• y = 40x - 6

To prepare for a recent road trip, Jill filled up her 19-gallon tank. She estimates that her SUV will use about three gallons per hour. Write an equation to model the amount of gasoline, G, remaining in her tank after t hours.

• G=19 – 3t

• G=19 + 3t

• G=3 - 19t

• G=3 + 19t

Bob's Plumbing charges $25 per hour plus a service fee of $40 for coming out to your house. Which equation models this situation?

• y = 25x + 40

• y = 40x + 25

• y = 25x

• y = 25x - 40

Eddie's Electric charges $90 per hour plus a $50 traveling fee. Which equation models this scenario?

• y = -50x + 90

• y = 90x + 50

• y = -90 - 50x

• y = 50 - 90x

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 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

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

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

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation

Amelia has $100 in her savings account and plans on saving $20 per week. Write an equation to represent this situation.

• y = 100x

• y = 20x

• y = 20x + 100

• y = 100x + 20

Charlie rented a moving truck. He paid a daily fee plus a per-mile fee to rent the truck. The equation below represents the daily amount Charlie paid for the truck if he drives it x miles.
y=0.5x+10
What does the slope of the graph of this equation represent?

• The daily fee for the moving truck

• The per-mile fee for the moving truck

• How much Charlie paid for the truck

• The number of miles he drove