© Teacher Created Materials Solving Systems of Equations Todays Lesson.

© Teacher Created Materials

Solving Systems of Equations

Today’s Lesson


Warm-Up Activity

We will warm up today by working with equations.


5x + 7 = 32– 7 – 7

5x = 25÷ 5 ÷ 5

x = 5

Solve the equation.

Check your answer using substitution. If the left and right side match, you have the correct answer.

5(5) + 7 = 3225 + 7 = 32

32 = 32


Solve and check your work using substitution.

3x – 7 = 14

x = 7

3(7) – 7 = 1421 – 7 = 14

14 = 14



x + 3 = –15

x = 27

(27) + 3 = –15– 18 + 3 = –15

–15 = –15

3

2

3

2



x – 8= 36

x = 176

(176) – 8 = 3644 – 8 = 36

36 = 36

4

1

4

1


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

Whole-Class Skills Lesson


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?

x = the number of Kimo’s cars

y = the number of Sadi’s cars

two equations


Write an equation for the total number of cars.

x + y = 8


x = the number of Kimo’s carsy = the number of Sadi’s cars


Write an equation for the amount of money spent for all the cars.

2x + 3y = 19





x + y = 8

Sub in for x to find y.

x y

2

3

4

5

6

5

43

x

y


2x + 3y = 19

Sub in for x to find y.

x y

3

4

5

6

4.33

3.66

32.33

x

y

x + y = 8

1

1

2

2

2x + 3y = 19


Where do the lines intersect?

x

y

x + y = 8

1

1

2

2

2x + 3y = 19

(5, 3)


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

x

y

x + y = 8

1

1

2

2

2x + 3y = 19 (5, 3)x = 5 y = 3Kimo has 5 cars.Sadi has 3 cars.




x + y = 8

Solve the system of equation without graphing. Remember you can use substitution.

2x + 3y = 19

We can rewrite the first equation so x is by itself on the left side of the equation.


x + y – y = – y + 8

Use inverse operations to get the x by itself.

Subtract y from both sides of the first equation.

x = – y + 8

x + y = 8


Substitute the new equation in for x.

x = – y + 8

2x + 3y = 19

2(– y + 8) + 3y = 19

– 2y + 16 + 3y = 19

y = 3


x = – (3) + 8

y = 3

x = 5

(5 , 3)


Write an equation for the total number of cards.

x + y = 64

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 cardsy = the number of Craig’s cards


Write an equation for the amount of money spent for all the cards.

4x + 2y = 184

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


x + y = 64

4(– y + 64) + 2y = 184

Solve the system by using substitution.

x = – y + 64

4x + 2y = 184

– 2y = – 72

y = 36


x + y = 64

If y = 36 then sub in to find x.

x + 36 = 64

x = 28

(28, 36)


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 cardsy = the number of Craig’s cards

(28, 36)

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

© Teacher Created Materials Solving Systems of Equations Todays Lesson.

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