Developing Equations

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5n + 0.5s = 78.5

  n + s = 87

• 1.5n + 0.5s = 78.5

  1.5n + 0.5s = 87

• n + s = 78.5

  1.5n + 0.5s =87

• n + s = 78.5

  n + s = 87

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  10x + 5y = 1430

• x + y = 49

  20x + 50y = 1430

• x + y = 49

  x + y = 1430

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

What point is a solution to the system of equations below?

3x + 2y = 16

7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4

• YES

• NO

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 (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

• d + n = 6.60

  0.10d + 0.05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  0.10d + 0.05n = 6.60

• d + n = 80

  0.10d + 0.5n = 6.60

Is the point (2, -1) a solution to the systems of equations below?

y=5x+3

y=-2x-4

• Yes

• No

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

Which equation matches the table?

• y = x + 5

• y = 5x

• y = x - 5

• x = y - 5

Which equation best represents the relationship between x and y in the table shown?

• y = 5x + 5

• y = 1/5x + 5

• y = 15x + 5

• y = 10x + 5