1. Section 7 – 2 Solving Systems Using Substitution
Objective:
To solve systems using substitution

2. Investigation: Estimating Solutions

4. Substitution Method:
A method for solving a system of equations in which one variable is replaced with an equivalent expression containing the other variable.
Example:
y = 3x + 2
4x + y = 9

5. Example 1 Using Substitution
A) Solve using substitution. y = -4x + 8 y = x + 7

6. B) Solve using substitution. y = 2x + 2 y = -3x + 4

7. C) Solve using substitution. y = 3x – 1 y = -2x + 4

8. D) Solve using substitution. y = 4x + 7 y = -3x

9. 1) y = x + 1 2) y = 2x + 5 y = 2x – 1 y = 6x + 1 3) 2y = x + 3 4) x – y = 1 x = y x = 1/2y + 2

10. Homework: Textbook Page 350; #5 – 10

12. Objective: To solve systems using substitution
Section 7 – 2 Continued…
Objective:
To solve systems using substitution

13. Example 2
A) Solve using substitution. 2y = x x = y

14. B) Solve using substitution. x – y = 1 x = 1/2y + 2

15. C) Solve using substitution. y = 2x 7x – y = 15

16. D) Solve using substitution. y = -3x + 4 2x – y = 6

17. SPECIAL CASES
Solve using substitution. 1) y = 3x – 6 2) x = y x + y = -6 y = x + 4

18. Classwork/Homework
7 – 2 Ditto: #1, 4, 7, 8, 9, 10

19. Answers to 7 – 1 Assignment
1) (1, 1) 4) (-3, 2) 7) (5, -2) 8) Infinitely Many 9) (100, 50) 10) No Solution

20. Section 7 – 2 Continued… (Day 3)
Objective:
To solve systems using substitution

21. Example 3 Using Substitution & the Distributive Property
A) Solve using substitution. 6x + 6y = -6 5x + y = -13

22. B) Solve using substitution. 3x + y = 4 2x – y = 6

23. C) Solve using substitution. -5x + y = - 2 -3x + 6y = -12

24. D) Solve using substitution. -2x + y = -1 4x + 2y = 12

25. E) Solve using substitution. 3y + 2x = 4 -6x + y = -7

26. F) Solve using substitution. 6y + 8x = 28 3 = 2x – y

27. Section 7 – 2 Continued… (Day 4)
Objective:
To solve systems using substitution

28. Example 4 Real-World Problem Solving
A) Your school committee is planning an after-school trip to take 193 students to a competition at another school. There are eight drivers available and two types of vehicles, school buses and minivans. The school buses seat 51 people each, and the minivans seat 8 people each. How many buses and minivans will be needed?

29. B). A youth group with 26 members is going to the beach
B) A youth group with 26 members is going to the beach. There will also be five chaperones that will each drive a van or a car. Each van seats 7 persons, including the driver. Each car seats 5 persons, including the driver. How many vans and cars will be needed?

30. C). A rectangle is 4 times longer than it is wide
C) A rectangle is 4 times longer than it is wide. The perimeter of the rectangle is 30 cm. Find the dimensions of the rectangle.

31. D). The length of a rectangle is 5 cm more than twice the width
D) The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is 34 cm. Find the dimensions of the rectangle.