Systems of Linear Equations in Context

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.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 

• x + y = 1550
  y  = 4x

• x + y = 1550
  y = x + 4

• y - x = 1550
  y = 4x

• y = 1550 + x
  y = x + 4

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?

• 4x + 7y = 578
  x + y = 3365

• 4x + 7y = 3365
  x + y = 578

• 4y + 7x = 578
  x + y = 3365

• 4y + 7x = 3365
  x + y = 578

What does the slope represent in this context?

• The height of the screw head above the wood before Tanvir rotated the screwdriver

• The number of millimeters per rotation that the screw height changes

• The number of rotations it takes to change the screw head height by 111 millimeter

• The number of rotations it takes to get the screw into the wood.

What does the slope represent in this context?

• The number of eggs that fit in the basket

• The mass per egg

• The mass of the basket

• Amount of eggs per basket

How many solutions?

• One solution

• No Solution

• Infinitely Many Solutions

Abby bought 2 slices of pizza and 3 bottles of water for $7.25. Billy bought 4 slices of pizza and 1 bottle of water for $8.25. What's the cost of a slice of pizza?

• $17.50

• $1.25

• $5

• $1.75

Gabe and Caden mow lawns for money. They are both saving money for a new game system. Gabe's savings, s , can be represented by the equation s = 40t + 50, where t is the time, in weeks, since he started saving. Caden's savings is given by the equation s = 35t + 100. Which statement correctly interprets the meaning of the solution to the system of equations in this context?

• Gabe and Caden both have $450 saved after 10 weeks of saving their money from mowing lawns.

• Gabe and Caden both have $170 saved after 2 weeks of saving their money from mowing lawns.

• Gabe and Caden both have $130 saved after 2 weeks of saving their money from mowing lawns.

• Gabe and Caden both have $10 saved after 450 weeks of saving their money from mowing lawns.

When solving a system of two linear equations algebraically, how can you tell if the system has exactly one solution?

• There will be one set of ordered pairs for each equation that make up the solution.

• There will be exactly one value for x and one value for y that makes both equations true.

• The algebraic process will result in a numerical statement that is always true.

• The algebraic process will result in a numerical statement that is never true.

Which ordered pair represents the solution to this system of linear equations?

• (4, 10000)

• (10000, 4)

• (8, 10000)

• (10000, 8)