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.