Name: Period: Date: · 2018. 11. 29. · 1 Name:___ Period:_Date:___ Proctor Hug HS Algebra 1 S1 Unit #4- Systems of Equations and Inequalities Learning Objectives 0 I can…

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Name:____________________________ Period:______________Date:_________

Proctor Hug HS Algebra 1 S1 Unit #4- Systems of Equations and Inequalities

Learning Objectives

I can…

Self-Rating 0 – I have no idea.

1 – I can solve problems but do not know why the math works.

2 – I understand why the math works

and can solve most problems but still make mistakes.

3 – I understand why the math works

and can accurately solve problems.

Evidence Cited

The evidence cited here must back-up your

self-rating claim.

PRE POST

Skill 1. I can solve systems of

equations by graphing


equations by substitution


equations by elimination

Skill 4. I can solve and graph linear

inequalities in two variables

Skill 5. I can solve systems of linear

inequalities

Monday Tuesday Wednesday Thursday Friday 15 - Oct 16 – Oct 17 - Oct 18 - Oct 19 - Oct

Solve by Graphing Solve by Graphing Quiz Solve by Graphing Solve by

Substitution

22 - Oct 23 - Oct 24 - Oct 25 – Oct 26 - Oct

Solve by Substitution

Solve by Substitution

Quiz

Solve by Elimination

No School

29 – Oct 30 – Oct 31 – Oct 1 – Nov 2 - Nov



Quiz

Graphing Linear Inequalities

Graphing Linear

Inequalities

5 - Nov 6 - Nov 7 - Nov 8 - Nov 9 - Nov

Graphing Linear Inequalities

No School Quiz System of Linear

Inequalities

System of Linear

Inequalities

12 - Nov 13 - Nov 14 - Nov 15 - Nov 16 - Nov

No School System of Linear

Inequalities Quiz Unit 5

Unit 5

2

Skill #1 I can solve systems of equations by graphing

Warm –Up

Create a line of best fit for the following

Graph the following line

𝒚 = −𝟐𝒙 + 𝟒

Guided Notes

Let’s practice graphing linear equations.

𝑦 = −2𝑥 − 4 𝑦 =1

2𝑥 + 6

Now let’s take both of those graphs, and put them onto one coordinate plane

What is a “solution to the system?”

3

You try!

Graph the linear equations and find the solution

𝑦 =1

2𝑥 − 2 𝑦 = 2𝑥 + 10

𝑦 = 3𝑥 − 7 𝑦 = −1

4𝑥 + 1

Review! Solve the following system algebraically:

5 − 3𝑥 = −3𝑥 − 4

What answer did we get? Why is this so? Let’s graph it and see!

𝑦 = 5 − 3𝑥 What is our slope for both

𝑦 = −3𝑥 − 4 equations? Remember, same

slope means

_________________________

4

You try! Solve the systems by graphing

𝑦 = −2𝑥 − 2 𝑦 = 𝑥

𝑦 = 3𝑥 − 7 𝑦 = 2𝑥

𝑥 + 𝑦 = −5 3𝑥 + 2𝑦 = −3

𝑦 =1

2𝑥 − 2 2𝑥 − 3𝑦 = −15

8𝑥 = 8 − 2𝑦 𝑦 = −2𝑥 + 2

−4𝑥 − 𝑦 = −4 𝑦 = −2𝑥 − 2

5

Describe and correct the error that was made when finding the solution to the system of

equations:

𝑦 + 3𝑥 = 9

𝑦 = 3𝑥 + 9

Roshaun has saved $150 and continues to add $10 each week. Keegan starts with $0

and saves $25 each week.

In how many weeks will they have the same amount of money?

How much money will they have saved?

Use the graph to determine the solution to the system

What is the approximate solution?

6

Ticket & Self Reflection

Please answer the question that is posed to all students prior to class ending. This is a formative assessment

technique engages all students and provides the all-important evidence of student learning for the teacher.

Gabriela considers buying fleece jackets from Anastasia’s Monograms or Monograms Unlimited. Anastasia’s

charges a one-time design fee and a price per jacket. Monograms Unlimited only charges a price per jacket.

Write and solve a system of equations to represent the cost for a jacket from each company.

What does the solution mean?

Gabriela needs to buy 10 jackets. Which company should she choose? How does the graph help her decide?

Explain?

7

Unit 3 Skill #2 I can solve systems of equations by substitution

Warm –Up

Evaluate/solve:

X=5 x=3 y=3x – 1

3x + 7 y=2x + 1 2y + 3

Guided Notes

The last thing we learned was how to solve systems by graphing. Now, we are going to

use a process called ________________________. This is when we take a solved variable

(x= or y=) and “substitute” that variable into the equation to solve for the opposite

variable. This will give us the same answer, but in a different way.

Use substitution to find the solution:

𝑥 = 𝑦 + 6 Notice how x is by itself?

𝑦 + 𝑥 = 10 This is what we are going to “substitute”

Now let’s graph to see that we will get the same answer that way to.

𝑥 = 𝑦 + 6

𝑦 + 𝑥 = 10

8

You try! Use substitution find the solution.

𝑦 = 6 − 𝑥 𝑥 = −𝑦 + 3

4𝑥 − 3𝑦 = −4 3𝑥 − 2𝑦 = −1

Sometimes, the equations do not already have a “solved” variable. We just need to get

one variable all by itself!

−3𝑥 − 𝑦 = 7 6𝑥 − 3𝑦 = −6

𝑥 + 2𝑦 = 6 𝑦 − 2 = 2𝑥

𝑦 = 2𝑥 − 4 𝑦 = 3𝑥 − 8

3𝑥 − 2𝑦 = 1 𝑦 = 13 − 4𝑥

9

Describe and correct the error made when finding the solution of the system

𝑥 = 2𝑦 − 4

5𝑥 − 3𝑦 = 1

Nate starts a lawn-mowing business. In his business, he has expenses and revenue.

Nate’s expenses are the cost of the lawn mower and gas, and his revenue is $25 per

lawn. At what point will Nate’s revenue exceed his expenses?

As part of her weekend job, Aisha went to the Snack Hut to pick up snacks and drinks

for her fellow workers. She purchased a total of 19 items and paid $64.25. How many

snacks and how many juices did she get?

10




Stay Fit gym charges a membership fee of $75. They offer karate classes for an

additional fee.

a. How many classes could members and non-members take before they pay the

same amount?

b. How much would they pay?

11

Unit 3 Skill #3 I can solve systems of equations by elimination

Warm –Up

Sadie and Micah used different methods to solve the system of equations.

In what ways are Sadie’s and Micah’s

approaches similar? In what ways are they

different?

Guided Notes

We have now discussed how to find a solution by graphing, and substitution. Now we

are going to learn about _________________________. This method involves

__________________ one of our variables. We must have the same coefficient with

____________________ signs.

Look at the following systems and determine if they have opposite variables. If yes,

what variable?

−𝑥 + 3𝑦 = 16 2𝑥 − 5𝑦 = 9 9𝑥 + 4𝑦 = 10 4𝑥 − 2𝑦 = 5

𝑥 + 6𝑦 = 12 7𝑥 + 𝑦 = 16 4𝑥 − 3𝑦 = 16 𝑥 + 2𝑦 = 3

If the answer was no, how can we change the problem to work for elimination?

12

Let’s find the solution of the following system using the elimination method.

𝑥 + 𝑦 = 7

2𝑥 − 𝑦 = 2

Now let’s take the same problem and find the solution using substitution

𝑥 + 𝑦 = 7

2𝑥 − 𝑦 = 2

Now, let’s graph!

𝑥 + 𝑦 = 7

2𝑥 − 𝑦 = 2

What did you notice about all 3 ways to find the solution?

13

You try! Use Elimination to find the solution.

4𝑥 − 2𝑦 = −2 𝑥 − 𝑦 = 4

3𝑥 + 2𝑦 = −12 2𝑥 + 𝑦 = 5

Sometimes we do not have opposite coefficients already, and we have to multiply

either one or both equations by something to make opposite coefficients

2𝑥 − 5𝑦 = 9 If we look at these equations, is there a variable that looks

7𝑥 + 𝑦 = 16 easier to eliminate than another? How would we do that?

9𝑥 + 4𝑦 = 10 What about these equations? These ones look harder.

4𝑥 − 3𝑦 = 16 we need to pick a variable to eliminate, and multiply

both equations to get opposite coefficients.

14

You try! Determine if we need to only multiply one equation, or both first!

3𝑥 + 2𝑦 = 4 4𝑥 − 3𝑦 = −9

3𝑥 + 6𝑦 = −24 3𝑥 + 2𝑦 = −11

3𝑥 + 2𝑦 = 8 𝑥 − 2𝑦 = 1

𝑥 + 4𝑦 = −4 2𝑥 + 3𝑦 = −12

7𝑥 − 4𝑦 = −12 4𝑥 − 3𝑦 = 17

𝑥 − 2𝑦 = 4 2𝑥 − 5𝑦 = 5

15

Describe and correct the error made when solving the system of equations

2𝑥 − 𝑦 = −1

𝑥 − 𝑦 = −4

Two pizzas and four sandwiches cost $62. Four pizzas and ten sandwiches cost $140.

How much does each pizza and sandwich cost?

At a clothing store, 3 shirts and 8 hats cost $65. The cost for 2 shirts and 2 hats is $30.

How much does each shirt and hat cost?

How does the structure of an equation determine which method is best to use when

solving (graphing, substitution, elimination)?

16




A florist is making regular bouquets and mini bouquets. The florist has 118 roses and

226 peonies to use in the bouquets. How many of each type of bouquet can the

florist make?

17

Unit 3 Skill #4 I can solve and graph linear inequalities in two variables

Warm –Up

Solve and graph graph

𝟑𝒙 − 𝟒 ≤ 𝟓 𝒚 =𝟏

𝟐𝒙 − 𝟔

Guided Notes

Now that we know how to graph inequalities with only one variable, and we know

how to graph linear equations, we are going to combine them together.

Graph the inequality:

𝑦 ≤ 𝑥 − 1 We will graph this how we normally do

Let’s remember how many answers

inequalities have. How can we show this?

What do we notice about the line of the graph

18

Let’s try another one:

𝑦 > 𝑥 − 1

What do we notice about this line?

What makes the lines different?

You try!

𝑦 < −3𝑥 + 5 𝑦 ≥ −3𝑥 + 5

𝑥 > 3 𝑦 ≤ 2

19

Describe and correct the error a student made when determining whether or not the

point (1, 1) is a solution to the inequality 𝑦 ≤ −4𝑥 + 5

Which inequality, 𝑦 >3

4𝑥 − 2 or 3𝑥 − 4𝑦 < 8, is shown by the graph? Explain.

A school has $600 to buy molecular sets for students to build models. A large kit is $23,

and a small kit is $12.

a. Write and graph an inequality that represents the number of each type of

molecular set the school can buy.

b. Suppose the school decides to buy 20 of the large kits. How many of the small kits

can the school now afford?

20




A freight elevator can hold a maximum weight of 2,500 points. A 180-pound person has a load of boxes to

deliver. Some of the boxes weigh 25 pounds each, and some weigh 60 pounds each.

a. Write and graph an inequality that represents the number of boxes the elevator can hold in one trip if the

person is not in the elevator.

b. Write and graph an inequality that represents the number of boxes the elevator can hold in one trip if the

person rides in the elevator.

c. Compare the graphs of the two inequalities

21

Skill #5 I can solve systems of linear inequalities

Warm –Up

Graph the points and find the slope solve the system by graphing

(-4, 7) and (-6, -4) 𝑦 = −5

3𝑥 + 3

𝑦 =1

3𝑥 − 3

Guided Notes

Graph the linear inequalities:

𝑦 > 𝑥 − 2 𝑦 ≤ −𝑥 + 1

Now let’s combine them onto one graph

What would our solution be?

22

You try! Watch for the symbols!

𝑦 = −2𝑥 + 1 𝑦 ≥ −2𝑥 + 1

𝑦 = 𝑥 + 2 𝑦 > 𝑥 + 2

How many solutions did the first graph have? How many solutions did the second

graph have? How can we tell?

Graph the system of inequalities

𝑦 ≥ −𝑥 + 2 𝑦 < 2𝑥

𝑦 < −𝑥 − 2 𝑦 > −3

Determine the inequalities based on the graph

23

Describe and correct the error a student made in writing the system of inequalities

represented by the graph shown below

Malia has $500 to purchase water bottles and pairs of socks for a fundraiser for her

school’s cross-country team. She needs to buy a total of at least 200 items without

buying too many of just one item. What graph shows the possible numbers of water

bottles and pairs of socks that Malia should buy?

24




A group of at most 10 people wants to purchase a combination of seats in Section A and Section B, but does

not want to spend more than $450. Graph the system of inequalities that represents the possible ticket

combinations they could buy. List 3 possible combinations they could buy.

Documents

Name: Period: Date: · 2018. 11. 29. · 1 Name:_____ Period:_____Date:_____ Proctor Hug HS Algebra 1 S1 Unit #4- Systems of Equations and Inequalities Learning Objectives 0 I can…

Name: Period: Date: · 2018. 11. 29. · 1 Name:___ Period:_Date:___ Proctor Hug HS Algebra 1 S1 Unit #4- Systems of Equations and Inequalities Learning Objectives 0 I can…