Section 7 – 2 Solving Systems

Using Substitution

Objective:To solve systems using substitution

Investigation: Estimating Solutions

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 + 24x + y = 9

Example 1 Using Substitution

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

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

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

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

1) y = x + 1 2) y = 2x + 5y = 2x – 1 y = 6x + 1

3) 2y = x + 3 4) x – y = 1x = y x = 1/2y + 2

Homework:Textbook Page 350; #5 – 10

Section 7 – 2 Continued…

Objective:To solve systems using substitution

Example 2

A) Solve using substitution. 2y = x + 3 x = y

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

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

D) Solve using substitution. y = -3x + 42x – y = 6

SPECIAL CASES

Solve using substitution.

1) y = 3x – 6 2) x = y + 4-3x + y = -6 y = x + 4

Classwork/Homework

7 – 2 Ditto: #1, 4, 7, 8, 9, 10

Answers to 7 – 1 Assignment

1) (1, 1)4) (-3, 2)7) (5, -2)8) Infinitely Many9) (100, 50)10) No Solution

Section 7 – 2 Continued…

(Day 3)

Objective:To solve systems using substitution

Example 3 Using Substitution & the Distributive Property

A) Solve using substitution. 6x + 6y = -65x + y = -13

B) Solve using substitution. 3x + y = 42x – y = 6

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

D) Solve using substitution. -2x + y = -14x + 2y = 12

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

F) Solve using substitution. 6y + 8x = 283 = 2x – y

Section 7 – 2 Continued…

(Day 4)

Objective:To solve systems using substitution

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?

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?

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.

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.