Systems of Equations Application

Systems of Equations Application

By Lesley Brantley

What does a solution to a system of equations look like?

What is the solution of the system graphed here?

What is the solution to the system graphed here?

What is the solution to the system graphed here?

What is the solution to the system graphed here?

Multiple Choice

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (0, 1)

Multiple Choice

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

Multiple Choice

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines

Multiple Choice

What is the solution?

• (6, 3)
• (3, 6)
• (-6, 3)
• No solution

Multiple Choice

The solution to this system is...

• (4, -2)
• (4, 2)
• (-2, 4) 
• (-4, -2)

Multiple Choice

What is the Solution to this system?

• (2,-2)
• (-2,2)
• All Real Numbers
• No Solution

This time we have to write TWO equations.

We already know how to write equations.

Application of Systems

Then we solve the system by graphing using Desmos and we have to explain what the solution means!

​The cost to rent a video game from Action Video is $2 plus $0.50 per day. The cost to rent a video game from TeeVee Rentals is $1 plus $0.75 per day. After how many days will the cost be the same? What is that cost?

​

Write a system of equations and solve. E​xplain what the solution means.

Lisa sold tickets for a local play. Children’s tickets cost $4 each and adult tickets cost $6 each. If 383 tickets were sold for a total of $2034, how many of each type of ticket were sold?

​Types of tickets:

​Super J-mart will sell 5 large jars and 2 small jars of their jelly for $19. They will also sell 2 large jars and 5 small jars for $16. What is the price of each jar?

Multiple Choice

August bought a total of 8 pounds of peanuts and cashews. Peanuts, p, cost $4 per pound and cashews, c, cost $6 per pound. The total amount August spent on the peanuts and cashews was $42. Which system of equations below could be solved to find how many pounds of peanuts and cashews August bought?

• p + c = 8

  4p + 6c = 42

• 4p + c = 8

  p + 6c = 42

• 4p + c = 42

  p + 6c = 8

• 4p + 6c = 8

  4p + 6c = 42

Multiple Choice

Your math test has 38 questions on it and is worth 200 points. The test consists of multiple-choice questions, x, wort 4 points each and open-ended questions, y, worth 20 points each. Which system of equations written below shows how you could find the number of each type of question?

• 4x + 20y = 38

  x + y = 200

• x - y = 200

  4x - 20y = 38

• x + y = 38

  4x + 20y = 200

• x - y = 38

  4x - 20y = 200

Multiple Choice

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.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6
• x + y = 4
  x - y = 6
• 4x + 6y = 13
  3x + 7y = 13.5
• 4x - 6y = 13
  3x - 7y = 13.5