REMEMBER FROM LAST CLASS
Transcript of REMEMBER FROM LAST CLASS
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
REMEMBER FROM LAST CLASS
Please grab a mini-whiteboard for you & your partner and a calculator if you don't have one. Save for later.
Find the POI of the two equations:
y = x + 4
2x + y = 16
Step 1 Combine 2 equations into 1 (by subbing 1 into the other) so that you only have one variable left
Step 4 State the final answer (x,y)
Step 3 Use the 1st variable to solve for the 2nd (sub it back into EITHER equation)
Step 2 Solve for the 1st variable
Remember that we are just finding the POINT where two LINES cross. Here is what it would look like if we graphed it.
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
If one basket has:
What would be the total of 2 baskets?
Each basket= 3 + 5 OR 3b + 5a
as a class
2 baskets of (3b + 5a) = 2 x (3b + 5a) = 2(3b + 5a)
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Expand and simplify
a) 2(3a + 8b) b) 5(x + 3)
whiteboard
e) (2x 1) 7 f) 8 5(y + 4)
(2x 1) 7 8 5(y + 4)
c) 3(4 y) d) 4(5 + 3y)
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Ex. Equations are given for the Carp & Richmond fairs.
How much did it cost?
whiteboard
C = 6rC = 4r + 10
After how many rides are the costs the same?
We can do substitution to answer word problems too..
Here's the solutions when we graph.
Carp: C = 6rRichmond: C = 4r + 10
Carp: C = 6rRichmond: C = 4r + 10
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Ex. James & Ethan both offer lawn-mowing services. After how many hours of work are the costs the same?
What is that cost?
whiteboard
C = 10h + 30C - 5h = 60
Here's the solutions when we graph.
C = 10h + 30C - 5h = 60
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Ex. The equations for two fairs are given below. Find the POI. What does it tell you about the fairs?
Fair 1: C = 3r + 5
Fair 2: C = r + 25
note2.2b Finding POI Using Substitution Day 2
Step 1 Combine 2 equations into 1 (by subbing 1 into the other) so that you only have one variable left
Step 2 Solve for the 1st variable
Step 3 Use the 1st variable to solve for the 2nd (sub it back into EITHER equation)
Step 4 State the final answer in context
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Ex. The equations for two fairs are given below. Find the POI. What does it tell you about the fairs?
Fair 1: C = 3r + 5
Fair 2: C = r + 25
note2.2b Finding POI Using Substitution Day 2
Step 1 Combine 2 equations into 1 (by subbing 1 into the other) so that you only have one variable left
Step 2 Solve for the 1st variable
Step 3 Use the 1st variable to solve for the 2nd (sub it back into EITHER equation)
Step 4 State the final answer in context
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Ex. Solve x = -2y + 8 and y = 4x -5
There are a couple extra complications in this one...
note
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Ex. Solve x = -2y + 8 and y = 4x -5
There are a couple extra complications in this one...
note
Option 1: Sub 2nd equation into 1st
Option 2: Sub 1st equation into 2nd
Ex. Solve x = -2y + 8 and y = 4x -5
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
Ex1. Solve the system of equations (AKA find the POI)
Answers: 1.a) (6, 40) b) (5,0) 2. Both fairs cost $34 after 7 rides.
Up at the whiteboards
b) x = -2y + 5 2x - 3y = 10
a) y = 5x + 10 y = 8x - 8
Ex2. The equations for two fairs are given below. Find the POI. What does it tell you about the fairs?
Fair 1: C = 4r + 6 Fair 2: C = 2r + 20
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
y = 5x + 10y = 8x - 8
1a)
b) x = ‐2y + 5 2x ‐ 3y = 10
Ex2. The equations for two fairs are given below. Find the POI. What does it tell you about the fairs?
Fair 1: C = 4r + 6
Fair 2: C = 2r + 20
2.2b Vertical Learning After Lesson
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
x = -3y + 73x - 2y = -12
Answer (-2, 3)
2.
Individual practice: Use substitution to solve the following problems.
Handout
y = -2x - 6y - 4x = 12
1.
Answer (-3, 0)
3. The equations for two jobs are given below. Where E is earning in $ and h is hours worked.Find the POI. What does it tell you about the jobs?
Job 1: E = 15h + 100Job 2: E = 25h Answer (10, 250)
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
1. y = ‐2x ‐ 6y ‐ 4x = 12
2.2b Individual Practice: Use substitution to solve the following questions.
x = ‐3y + 7
3x ‐ 2y = ‐122.
3. The equations for two jobs are given below. Where E is earning in $ and h is hours worked.Find the POI. What does it tell you about the jobs?
Job 1: E = 15h + 100
Job 2: E = 25h
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2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020
HW: Go back over your worksheet & complete any unfinished questions