remember from last class

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.


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)


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)


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


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


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


Ex. Solve x = -2y + 8 and y = 4x -5

There are a couple extra complications in this one...

note



There are a couple extra complications in this one...

note

Option 1: Sub 2nd equation into 1st

Option 2: Sub 1st equation into 2nd



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


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


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)


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


HW: Go back over your worksheet & complete any unfinished questions

remember from last class

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