How do you use systems of equations to help solve word problems?

How do you use systems of equations to help solve word

problems? For example, You buy 7 bags of gummy bears and 3 bags of chocolate costs $22. 3 bags of gummy bears

and 1 bag of chocolate costs $8. What is the price of a bag of gummy bears and a bag of chocolate?

In this lesson you will learn how to solve word problems by

using systems of equations.

Let’s Review-3x + 7y = -16-9x + 5y = 16

-3( ) -3( ) 9x – 21y = 48-9x + 5y = 16 +

-16y = 64 x x -1

16-116

y = -4

-9x + 5(-4) = 16-9x – 20 = 16

+20 +20-9x = 36

x x -19

-19x = -4

(-4,-4)

Core Lesson You and a friend are at the store and want to buy

some candy. You buy 7 bags of gummy bears and 3 bags of chocolate and your total is $22. Your friend buys 3 bags of gummy bears and 1 bag of chocolate and her total is $8. What is the price of a bag of gummy bears and a bag of chocolate?

Your candyFriend’s candy

x y

7x + 3y = 22 3x + y = 8

Core Lesson 7x + 3y = 22

3x + y = 8 -3( ) -3( ) -9x – 3y = -24 7x + 3y = 22 +

-2x = -2 x x -1

2-12x = 1

7(1) + 3y = 227 + 3y = 22

-7 -73y = 15

x x 13

13

y = 5 (1,5)

7(1) + 3(5) = 22 3(1) + 5 = 8

In this lesson you have learned how to solve word problems by solving systems of equations.

Guided Practice

The difference of two numbers is 3 and their sum is 13. What are the two numbers?

Extension Activities

Write a word problem based on the following system. Then, solve the system by using both substitution and linear combination (elimination) and write what your answer means in terms of your question.

3x + y = 383x + 2y = 52

Extension Activities

Describe another extension activity here…

Extension Activities

Describe a third extension activity here if you have a good one…

Quick Quiz The sum of two numbers is 12 and their difference is 4. What are the two numbers?

Your school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school made $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?