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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