Warm – up #2 1. y< 3 2 𝑥−6 x≤4

Homework Log Fri 10/16 Lesson 3 – 2 Learning Objective: To solve systems algebraically Hw: Pg. 146 #10, 16, 17, 23-39 odd

10/10&11/17 Lesson 3 – 2 Solving Systems Algebraically Algebra II

Learning Objective To solve systems by substitution To solve systems by elimination

Solve by Substitution 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

Solutions of Systems 0 = 5  Never True!! No Solution Parallel Lines 5 = 5  Always True!! Infinite Solutions Same Line

Solve by Substitution x – 7y = 11 1. 𝑥−7𝑦=11 5𝑥+4𝑦=−23 +7y +7y 1. 𝑥−7𝑦=11 5𝑥+4𝑦=−23 5(7y + 11) + 4y = - 23 35y + 55 + 4y = - 23 39y = - 78 y = -2 x – 7(-2) = 11 x + 14 = 11 x = -3 Now plug y = -2 into either equation to solve for x. (-3, -2)

Solve by Substitution -2x + y = 3 2. 2𝑥−𝑦=−6 −2𝑥+𝑦=3 +2x +2x 2. 2𝑥−𝑦=−6 −2𝑥+𝑦=3 2x – (2x + 3) = - 6 2x – 2x – 3 = -6 -3 = -6 No Solution! Lines are parallel & will never intersect!

Solve by Substitution 5x + y = -5 3. 6𝑥+2𝑦=−10 5𝑥+𝑦=−5 -5x -5x 3. 6𝑥+2𝑦=−10 5𝑥+𝑦=−5 6x + 2(-5x – 5) = -10 6x – 10x – 10 = -10 -4x = 0 x = 0 6(0) + 2y = -10 2y = -10 y = - 5 (0, -5)

Solve by Elimination 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. 4𝑥+2𝑦=9 −4𝑥+3𝑦=16 5y = 25 y = 5 4x + 2(5) = 9 4. 4𝑥+2𝑦=9 −4𝑥+3𝑦=16 Since “x” already have opposite coefficients of 4 and -4, just add straight down 5y = 25 y = 5 4x + 2(5) = 9 4x + 10 = 9 4x = -1 x=− 1 4 (− 1 4 , 5)

Solve by Elimination −6𝑥−𝑦=27 6𝑥+16𝑦=18 5. −6𝑥−𝑦=27 3𝑥+8𝑦=9 (2)( ) (2) 5. −6𝑥−𝑦=27 3𝑥+8𝑦=9 −6𝑥−𝑦=27 6𝑥+16𝑦=18 (2)( ) (2) 15y = 45 y = 3 3x + 8(3) = 9 3x + 24 = 9 3x = -15 x = -5 (-5, 3)

Solve by Elimination 6𝑥−5𝑦=−8 −4𝑥+5𝑦=12 6. 6𝑥−5𝑦=−8 4𝑥−5𝑦=−12 6. 6𝑥−5𝑦=−8 4𝑥−5𝑦=−12 6𝑥−5𝑦=−8 −4𝑥+5𝑦=12 (-1)( ) (-1) 2x = 4 x = 2 6(2) – 5y = -8 12 – 5y = -8 -5y = -20 y = 4 (2, 4)

Solve by Elimination (-3)( ) (-3) 7. 5𝑥+3𝑦=52 15𝑥+9𝑦=54 0 = -102 (-3)( ) (-3) 7. 5𝑥+3𝑦=52 15𝑥+9𝑦=54 −15𝑥−9𝑦=−156 15𝑥+9𝑦=54 0 = -102 Parallel Lines! No Solution

Solve by Elimination (-3)( ) (-3) −6𝑥−9𝑦=−15 6𝑥+9𝑦=15 (-3)( ) (-3) 8. 2𝑥+3𝑦=5 6𝑥+9𝑦=15 −6𝑥−9𝑦=−15 6𝑥+9𝑦=15 0 = 0 Same Line! Infinite Solutions

Solve by Elimination (-4)( ) (-4) 9. 4𝑥+3𝑦=12 −6𝑥+4𝑦=−1 (3)( ) (3) (-4)( ) (-4) 9. 4𝑥+3𝑦=12 −6𝑥+4𝑦=−1 −16𝑥−12𝑦=−48 −18𝑥+12𝑦=−3 (3)( ) (3) -34x = -51 x = 3 2 4( 3 2 ) + 3y = 12 6 + 3y = 12 3y = 6 y = 2 ( 3 2 , 2)

Solve by Elimination (-3)( ) (-3) 10. 2𝑥+7𝑦=4 3𝑥+5𝑦=−5 (-3)( ) (-3) 10. 2𝑥+7𝑦=4 3𝑥+5𝑦=−5 −6𝑥−21𝑦=−12 6𝑥+10𝑦=−10 (2)( ) (2) -11y = -22 y = 2 2x + 7(2) = 4 2x + 14 = 4 2x = -10 x = -5 (-5, 2)

Word Problem 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 store b) When would it cost the same? c) When do you use online vs. local?

Word Problem Solve by substitution 𝑦=0.15𝑥+2.70 𝑦=0.25𝑥 0.25x = 0.15x + 2.70 0.10x = 2.70 x = 27 photos would cost both $6.75 Use online store if more than 27 photos. Use local store if less than 27 photos.

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