1. Warm – up #2
1. y< 3 2 𝑥−6 x≤4

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

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

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

5. 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

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

7. 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 y = - 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)

8. 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!

9. 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)

10. 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

11. 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)

12. 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)

13. 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)

14. 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

15. 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

16. 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)

17. 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)

18. 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?

19. Word Problem Solve by substitution 𝑦=0.15𝑥+2.70 𝑦=0.25𝑥
0.25x = 0.15x
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.

20. 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?

21. Assignment: Pg. 146 #10, 16, 17, odd