Applications of Systems of Equations

Description: This lesson introduces the concept of using systems of equations to solve real-world problems. We will explore how to set up and solve systems of equations based on various scenarios.

Outline

Introduction to Systems of Equations
Setting Up Systems of Equations
Solving Systems Using Substitution
Solving Systems Using Elimination
Real-World Applications
Examples and Exercises
Homework and Revision

Examples

Example 1

Problem: Sarah and John are selling tickets for a charity event. Sarah sells tickets for $5 each and John sells tickets for $7 each. Together, they sold 50 tickets and raised $320. How many tickets did each person sell?

Solution: Let x be the number of tickets Sarah sold and y be the number of tickets John sold. We have the following system of equations:

x + y = 50
5x + 7y = 320

Solving these equations, we find that Sarah sold 20 tickets and John sold 30 tickets.

Exercises

Exercise 1

Problem: A bakery sells muffins and cookies. Muffins cost $3 each and cookies cost $2 each. If 60 items were sold for a total of $150, how many muffins and cookies were sold?

Solution: Let x be the number of muffins and y be the number of cookies. The system of equations is:

x + y = 60
3x + 2y = 150

Solve these equations to find the number of muffins and cookies sold.

Homework

Complete the following problems:

Problem 1: A bookstore sells notebooks for $8 each and pens for $2 each. If a student bought 15 items and spent $80, how many notebooks and pens did the student buy?
Problem 2: Two friends are purchasing concert tickets. One friend buys tickets for $12 each and the other buys tickets for $15 each. If they buy a total of 10 tickets and spend $126, how many tickets did each friend buy?

Revision

Review the steps for solving systems of equations:

Identify the variables and set up the system of equations.
Choose a method (substitution, elimination) to solve the system.
Check your solution by substituting the values back into the original equations.