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.

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)

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)

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

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

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

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

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

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

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

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

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)

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

2.2b NEW DAY Substitution day 2 and distributive prop.notebook March 11, 2020

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