Download presentation

Presentation is loading. Please wait.

1
**Solving Systems of Equations**

Today’s Lesson Solving Systems of Equations

2
Warm-Up Activity We will warm up today by working with equations.

3
**5x + 7 = 32 5(5) + 7 = 32 25 + 7 = 32 32 = 32 Solve the equation.**

– 7 – 7 5x = 25 ÷ ÷ 5 x = 5 Check your answer using substitution. If the left and right side match, you have the correct answer. 5(5) + 7 = 32 = 32 32 = 32

4
**Solve and check your work using substitution.**

3x – 7 = 14 x = 7 3(7) – 7 = 14 21 – 7 = 14 14 = 14

5
**Solve and check your work using substitution.**

x + 3 = –15 x = 27 (27) + 3 = –15 – = –15 –15 = –15

6
**Solve and check your work using substitution.**

x – 8= 36 x = 176 (176) – 8 = 36 44 – 8 = 36 36 = 36

7
**Whole-Class Skills Lesson**

Today, you will solve systems of two linear equations with two variables using the substitution method.

8
Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have? How many equations can be written from the information in the problem? two equations x = the number of Kimo’s cars y = the number of Sadi’s cars

9
**x + y = 8 Write an equation for the total number of cars.**

Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have? x = the number of Kimo’s cars y = the number of Sadi’s cars Write an equation for the total number of cars. x + y = 8

10
Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have? x = the number of Kimo’s cars y = the number of Sadi’s cars Write an equation for the amount of money spent for all the cars. 2x + 3y = 19

11
x + y = 8 y x y 2 3 4 5 6 5 4 3 x Sub in for x to find y.

12
**2x + 3y = 19 4.33 3.66 3 2.33 Sub in for x to find y. x y 3 4 5 6 y**

13
**Where do the lines intersect?**

y x + y = 8 (5, 3) 2x + 3y = 19 2 1 x 1 2

14
**What does the point, (5, 3) represent?**

x = the number of Kimo’s cars y = the number of Sadi’s cars y x + y = 8 What does the point, (5, 3) represent? (5, 3) 2x + 3y = 19 x = y = 3 Kimo has 5 cars. Sadi has 3 cars. 2 1 x 1 2

15
**Solve the system of equation without graphing**

Solve the system of equation without graphing. Remember you can use substitution. x + y = 8 2x + 3y = 19 We can rewrite the first equation so x is by itself on the left side of the equation.

16
**Use inverse operations to get the x by itself.**

Subtract y from both sides of the first equation. x + y = 8 x + y – y = – y + 8 x = – y + 8

17
**2x + 3y = 19 2(– y + 8) + 3y = 19 – 2y + 16 + 3y = 19 y = 3**

Substitute the new equation in for x. x = – y + 8 2x + 3y = 19 2(– y + 8) + 3y = 19 – 2y y = 19 y = 3

18
y = 3 x = – (3) + 8 x = 5 (5 , 3)

19
**x + y = 64 Write an equation for the total number of cards.**

Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. How many baseball cards do each of the boys have? x = the number of Chad’s cards y = the number of Craig’s cards Write an equation for the total number of cards. x + y = 64

20
**Chad and Craig have 64 baseball card all together**

Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. Together they have spent a total of $184. How many baseball cards do each of the boys have? x = the number of Chad’s cards y = the number of Craig’s cards Write an equation for the amount of money spent for all the cards. 4x + 2y = 184

21
**Solve the system by using substitution.**

x + y = 64 x = – y + 64 4x + 2y = 184 4(– y + 64) + 2y = 184 – 2y = – 72 y = 36

22
**If y = 36 then sub in to find x.**

x + y = 64 x + 36 = 64 x = 28 (28, 36)

23
**Chad has 28 baseball cards and Craig has 36 baseball cards.**

Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. How many baseball cards do each of the boys have? x = the number of Chad’s cards y = the number of Craig’s cards (28, 36) Chad has 28 baseball cards and Craig has 36 baseball cards.

Similar presentations

Presentation is loading. Please wait....

OK

4.7 Complete the Square.

4.7 Complete the Square.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on sound navigation and ranging system of a down Ppt on computer science projects Ppt on aerobics classes Ppt on history of olympics for children Ppt on time management for engineering students Ppt on group development forming Ppt on ac to dc converter Ppt on principles of object-oriented programming language Ppt on operating system deadlock Open ppt on ipad 2