10/16/15 Fri HW: Pg. 146 #10, 16, 17, 23-39 odd
WARM3– UP #2
1. y < 𝑥 − 6
2
x≤4
HOMEWORK LOG
Fri
Learning Objective:
To solve systems algebraically
10/16
Lesson
3–2
Hw: Pg. 146 #10, 16, 17, 23-39
odd
LESSON 3 – 2 SOLVING
SYSTEMS ALGEBRAICALLY
Algebra 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 SUBSTITUTION x – 7y = 11
𝑥 − 7𝑦 = 11
1.
5𝑥 + 4𝑦 = −23
substitute
5(7y + 11) + 4y = - 23
35y + 55 + 4y = - 23
39y = - 78
y = -2
+7y +7y
x = 7y + 11
Modified/isolated version
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
2𝑥 − 𝑦 = −6
2.
−2𝑥 + 𝑦 = 3
substitute
2x – (2x + 3) = - 6
2x – 2x – 3 = -6
-3 = -6
No Solution!
+2x
+2x
y = 2x + 3
Modified/isolated version
Lines are parallel &
will never
intersect!
SOLVE BY SUBSTITUTION 5x + y = -5
6𝑥 + 2𝑦 = −10
3.
5𝑥 + 𝑦 = −5
substitute
6x + 2(-5x – 5) = -10
6x – 10x – 10 = -10
-4x = 0
x=0
-5x
-5x
y = -5x - 5
Modified/isolated version
6(0) + 2y = -10
2y = -10
y=-5
(0, -5)
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 ELIMINATION
4𝑥 + 2𝑦 = 9
4.
−4𝑥 + 3𝑦 = 16
5y = 25
y=5
4x + 2(5) = 9
4x + 10 = 9
4x = -1
x=
1
−
4
Since “x” already
have opposite
coefficients of 4 and
-4, just add straight
down
1
(− ,
4
5)
Eliminate x (try to get -6x and +6x)
SOLVE BY ELIMINATION
−6𝑥 − 𝑦 = 27
5.
(2)(3𝑥 + 8𝑦) = 9 (2)
−6𝑥 − 𝑦 = 27
6𝑥 + 16𝑦 = 18
15y = 45
y=3
(-5, 3)
3x + 8(3) = 9
3x + 24 = 9
3x = -15
x = -5
Eliminate y (try to get -5y and +5y)
SOLVE BY ELIMINATION
6𝑥 − 5𝑦 = −8
6.
(-1)(4𝑥 − 5𝑦 )= −12 (-1)
6𝑥 − 5𝑦 = −8
−4𝑥 + 5𝑦 = 12
2x = 4
x=2
(2, 4)
6(2) – 5y = -8
12 – 5y = -8
-5y = -20
y=4
SOLVE BY ELIMINATION – JUST WATCH
(-3)(5𝑥 + 3𝑦 )= 52 (-3)
15𝑥 + 9𝑦 = 54
−15𝑥 − 9𝑦 = −156
15𝑥 + 9𝑦 = 54
0 = -102
No Solution
Parallel Lines!
SOLVE BY ELIMINATION – JUST WATCH
(-3)(2𝑥 + 3𝑦) = 5 (-3)
6𝑥 + 9𝑦 = 15
−6𝑥 − 9𝑦 = −15
6𝑥 + 9𝑦 = 15
0=0
Infinite Solutions
Same Line!
SOLVE BY ELIMINATION
(-4(4𝑥 + 3𝑦 )= 12 (-4)
7.
(3)(−6𝑥 + 4𝑦 )= −1(3)
−16𝑥 − 12𝑦 = −48
−18𝑥 + 12𝑦 = −3
-34x = -51
x=
3
( ,
2
2)
3
4( )
2
3
2
+ 3y = 12
6 + 3y = 12
3y = 6
y=2
SOLVE BY ELIMINATION– JUST WATCH
(-3)( 2𝑥 + 7𝑦) = 4(-3)
10.
(2)( 3𝑥 + 5𝑦 )= −5 (2)
−6𝑥 − 21𝑦 = −12
6𝑥 + 10𝑦 = −10
-11y = -22
y=2
(-5, 2)
2x + 7(2) = 4
2x + 14 = 4
2x = -10
x = -5
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
𝑦 = 0.15𝑥 + 2.70
a)
𝑦 = 0.25𝑥
Solve by
substitution
b) 0.25x = 0.15x + 2.70
0.10x = 2.70
x = 27 photos would cost both $6.75
c) 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