WARM – UP #2 10/16/15 Fri HW: Pg. 146 #10, 16, 17, 23-39 odd.

WARM – UP #21.

10/16/15 Fri HW: Pg. 146 #10, 16, 17, 23-39 odd

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

ALGEBRAICALLYAlgebra II

LEARNING OBJECTIVE

To solve systems by substitution To solve systems by elimination

Because I know this!!!

SOLUTIONS OF SYSTEMS 0 = 5 Never True!!

No Solution Parallel Lines

5 = 5 Always True!!Infinite Solutions Same Line

SOLVE BY SUBSTITUTION Get a variable by itself in one equation (ISOLATE)

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 SUBSTITUTION1. x – 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)

Modified/isolated version

substitute

SOLVE BY SUBSTITUTION2. -2x + y = 3

+2x +2xy = 2x + 3

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

Lines are parallel & will never intersect!


substitute

SOLVE BY SUBSTITUTION3. 5x + 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)


substitute

SOLVE BY ELIMINATION Pick one variable and get opposite coefficients (Ex: 5x & -5x)

Line up variables

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 ELIMINATION4.

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)


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

15y = 45y = 3

(-5, 3)

(2)( ) (2)

Eliminate x (try to get -6x and +6x)


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

2x = 4x = 2

(2, 4)

(-1)( ) (-1)

Eliminate y (try to get -5y and +5y)

SOLVE BY ELIMINATION – JUST WATCH

Parallel Lines!

0 = -102

No Solution

(-3)( ) (-3)

SOLVE BY ELIMINATION – JUST WATCH

Same Line!

0 = 0

Infinite Solutions

(-3)( ) (-3)


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

-34x = -51x =

(, 2)

(3)( ) (3)(-4( ) (-4)

SOLVE BY ELIMINATION– JUST WATCH10.

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

-11y = -22y = 2

(-5, 2)

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

WORD PROBLEM11. 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 store

b) When would it cost the same?

c) When do you use online vs. local?

WORD PROBLEMa)

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

b) 0.25x = 0.15x + 2.70 0.10x = 2.70x = 27 photos would cost both $6.75

Solve by substitution

TICKET OUT THE DOOR 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?

ASSIGNMENT:

PG. 146 #10, 16, 17,23-39 ODD

WARM – UP #2 10/16/15 Fri HW: Pg. 146 #10, 16, 17, 23-39 odd.

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