Warm Up – Tuesday, November 17th
Solve for x: 3𝑥 + 2 + 5𝑥 = 18
Graph : y = -2x -3
Solve for a: 4𝑎 + 3 = 10 – 3𝑎
Warm
Write a system of equations that matches the
description: Hannah bought candy grams for her friends
for $2 each and valentines cards for $.50 each. Altogether
she sent 22 cards and candy grams and spent $38.
5.Bonus! Solve the system above.
1.
2.
3.
4.
Up!
1
This Week in Work (TWIW)
•Homework due Thursday
•Classwork due Monday, 11/23
•Quiz Tuesday 11/24
•Projects due 12/3
2
Tutoring
Morning
(8:05 – 8:40 AM)
Afternoon
(4:15 – 4:45 PM)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
9AM - Noon
3
Goal
SWBAT solve a system of equations
using substitution that involve
distribution. (A.8B)
Our Goals This Week:
DOL
75%
Why This Matters
Over the past 2 days, we have started to learn
how write systems of equations to help us solve
real world equations. Today we will explore one
method to solve systems of equations. This all
matters because many things in our world have
multiple constraints on them (meaning you need
to use system of equations).
4
variable
equation
REPLACE
5
Example 1
Total amount earned, y
Total number of days, x
e = 2t + 3
e = 1t + 5
= 1(2) + 5 = 7
Set them equal to each other
2t + 3 = 1t + 5
-1t
-1t
t+3=5
-3 -3
t =2
2
7
2
7
6
This is sewius.
7
Example 2
d
C
Total number of ducks, x
Total number of cows, y
d + c = 93
2d + 4c = 208
2( 93 – c ) + 4c = 208
186 – 2c + 4c = 208
d + c = 93
- c -c
d = 93 – c
d = 93 – 11
d = 82
186 + 2c = 208
2c = 22
c = 11
8
Problem 3
=2–1 =1
6x – 11 = x – 1
-1x
-1x
5x – 11 = -1
+11 +11
5x = 10
x =2
(2, 1)
9
Problem 4
3( -4y – 8) – 5y = 10
-12y – 24 – 5y = 10
– 17y – 24 = 10
x + 4y = -8
- 4y -4y
x = -4y – 8
= -4(-2) – 8
=8–8
x=0
– 17y = 34
y = -2
(2, 1)
(0, -2)
10
Problem 5
2x = 3y – 7
𝟑
𝟕
𝒙= 𝒚 −
𝟐
𝟐
(2, 1)
𝟑
𝟕
= (𝟑) −
𝟐
𝟐
𝟗 𝟕
=
−
𝟐 𝟐
𝟐
= =𝟏
(0, -2)
𝟐
5(
2(
𝟑
𝒚
𝟐
𝟏𝟓
𝒚
𝟐
𝟕
− )
𝟐
𝟑𝟓
−
𝟐
– 4y = -7
– 4y = -7)
1𝟓𝐲 − 𝟑𝟓 – 8y = -14
7𝐲 − 𝟑𝟓 = -14
7𝐲 = 21
(1, 3)
𝐲 =3
11
White Board
= 6(2) – 11 = 12 – 11
=1
-2x – 3( 6x – 11) = - 7
-2x – 18x + 33 = - 7
– 20x + 33 = - 7
– 20x = - 40
x =2
(2, 1)
12
White Boards
= (4) – 1 = 3
2x – 3( x – 1 ) = - 1
2x – 3x + 3 = - 1
–x+3 =-1
–x =-4
x =4
(2, 1)
(4, 3)
13
White Board
(2, 1)
(4, 3)
14
Independent practice
Directions
• Complete at least 1 more
problem on the front
• Complete 8 problems on back
• If you have a question, ASK!
• Check work at the board, help
your neighbor
$175
15
Common Mistakes
16
Common Mistakes
17
Common Mistakes
18
DOL
1. y = -3x + 3
7x + 2y = 1
2. x = 2y – 25
3x – y = 0
19