Linear system: real-life situations and solutions

Objectives
Student will be able to:
  • develop and write systems of linear equations to represent real-life situations.
  • solve systems of linear equations by graphing using technology when appropriate.
  • determine whether a system of linear equations has one solution, no solution, or infinitely many solutions by graphing and interpret the solution in a real-life situation.

Exercises

Use a graphing calculator or the blank graph provided to complete the exercises. Show all work.

1.
Burger Palace currently has four customers in line and the number of customers is increasing at a rate of two people per minute. Hot-dog Hut has one customer in line and the number of customers is increasing at a rate of three people per minute. Develop a system of linear equations to represent the number of customers in each line.
 
system of equations:
 
 
(variables used may vary)
Check student's work.
1.
 

2.
Use the graphing method to graph the linear system in the previous exercise. Predict when the number of customers in each line will be the same. (Find the point of intersection.)
 
 
The number of customers will be the same after three minutes.
Check student's work.
2.
 

3.
The perimeter of a rectangle is 12 cm. The length of the rectangle is 2 cm more than the width. Write a linear system and use the graphing method to determine the dimensions of the rectangle.
 
The system of linear equations:
 
 
The length of the rectangle is 4cm and the width of the rectangle is 2cm. 
Check student's work.
3.
 

4.
The cost of four colas and one hot-dog is $7. The cost of two colas and two hot-dogs is $8. What is the cost of one cola? What is the cost of one hot-dog?
 
The cost of one cola is $1.
The cost of one hot-dog is $3.
Check student's work.
4.
 

5.
Mrs. Gorski took her children to see a movie. She paid for two child tickets and one adult ticket and spent a total of $17. Mrs. Rivera also saw a movie with one child and paid a total of $12. Develop and solve a system of linear equations to determine the cost of one child's ticket.
 
One child's ticket costs $5.00.
Check student's work.
5.