Post on 18-Jan-2016
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!
Modified/isolated version
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)
Modified/isolated version
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)
SOLVE BY ELIMINATION5.
3x + 8(3) = 93x + 24 = 93x = -15x = -5
15y = 45y = 3
(-5, 3)
(2)( ) (2)
Eliminate x (try to get -6x and +6x)
SOLVE BY ELIMINATION6.
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)
SOLVE BY ELIMINATION7.
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