1.

Warm – up #2

Homework Log

Fri

10/16

Lesson 3 – 2

Learning Objective: To solve systems algebraically

Hw: Pg. 146 #10, 16, 17, 23-39 odd

Lesson 3 – 2 Solving Systems Algebraically

Algebra II

To solve systems by substitution

To solve systems by elimination

Learning Objective

0 = 5 Never True!! ◦No Solution ◦Parallel Lines

5 = 5 Always True!!◦Infinite Solutions ◦Same Line

Solutions of Systems

Get a variable by itself in one equation

Plug into other equation to solve

Plug solved variable back into one eq’n to solve for other variable

Solution is where the two lines will intersect

Solve by Substitution

1.

Solve by Substitutionx – 7y = 11 +7y +7yx = 7y + 11

5(7y + 11) + 4y = - 23 35y + 55 + 4y = - 2339y = - 78y = -2

Now plug y = -2 into either equation to solve for x.

x – 7(-2) = 11x + 14 = 11x = -3

(-3, -2)

2.

Solve by Substitution-2x + y = 3+2x +2xy = 2x + 3

2x – (2x + 3) = - 62x – 2x – 3 = -6-3 = -6No Solution!

Lines are parallel & will never intersect!

3.

Solve by Substitution5x + y = -5-5x -5xy = -5x - 5

6x + 2(-5x – 5) = -106x – 10x – 10 = -10-4x = 0x = 0

6(0) + 2y = -102y = -10y = - 5

(0, -5)

Pick one variable and get opposite coefficients

Add straight down & solve

Plug solved variable back into one eq’n to solve for other variable

Solution is where the two lines will intersect

Solve by Elimination

4.

Solve by Elimination

4x + 2(5) = 94x + 10 = 94x = -1

5y = 25y = 5

Since “x” already have opposite coefficients of 4 and -4, just add straight down

(, 5)

5.

Solve by Elimination

3x + 8(3) = 93x + 24 = 93x = -15x = -5

15y = 45y = 3

(-5, 3)

(2)( ) (2)

6.

Solve by Elimination

6(2) – 5y = -812 – 5y = -8-5y = -20y = 4

2x = 4x = 2

(2, 4)

(-1)( ) (-1)

7.

Solve by Elimination

Parallel Lines!

0 = -102

No Solution

(-3)( ) (-3)

8.

Solve by Elimination

Same Line!

0 = 0

Infinite Solutions

(-3)( ) (-3)

9.

Solve by Elimination

4() + 3y = 126 + 3y = 123y = 6y = 2

-34x = -51x =

(, 2)

(3)( ) (3)

(-4)( ) (-4)

10.

Solve by Elimination

2x + 7(2) = 42x + 14 = 42x = -10x = -5

-11y = -22y = 2

(-5, 2)

(2)( ) (2)(-3)( ) (-3)

11. An online photo store charges $0.15/photo plus $2.70 shipping.A local store charges $0.25 with no shipping.a) Write a cost eq’n for each storeb) When would it cost the same?c) When do you use online vs. local?

Word Problem

𝑦=0.15 𝑥+2.70𝑦=0.25 𝑥

Word Problem

Use online store if more than 27 photos.Use local store if less than 27 photos.

0.25x = 0.15x + 2.700.10x = 2.70x = 27 photos would cost both $6.75

Solve by substitution

You work for Alg Comp delivering packages. Alg Comp pays you a flat rate of $9.50 per hour. Geo Comp pays employees $2 per hour plus $3 per delivery. How many deliveries would Geo Comp’s employees have to make in four hours to earn the same pay you earn in a four-hour shift?

Ticket Out the Door

Assignment:

Pg. 146 #10, 16, 17, 23-39 odd