ALGEBRA 1 – UNIT 12: SYSTEMS OF LINEAR EQUATIONS · ALGEBRA 1 – UNIT 12 · WEEK 7 · SYSTEMS OF LINEAR EQUATIONS NOTES & PRACTICE PAGE 5 Solving Systems of Linear Equations Using

Name:__________________________________________ Date:_____________________ Period:_____

ALGEBRA 1 – UNIT 12 · WEEK 7 · SYSTEMS OF LINEAR EQUATIONS NOTES & PRACTICE PAGE 1

ALGEBRA 1 – UNIT 12: SYSTEMS OF LINEAR EQUATIONS Key Dates

Quiz: Block Day, February 19-20, 2014

Test: Tuesday, February 25, 2014 Day 1 (Monday, February 17, 2014)

Solving Systems of Equations through Graphing and Tables ☺ " Test I can graph a linear equation in slope intercept form. N/A

I can solve a linear equation in standard form for y to put it in slope intercept form. N/A

I can find the intersecting point of two lines and identify it as the solution of the system of equations. /7

I can recognize that parallel lines have no solution to their system. /1 I can recognize that lines with the same slope and intercept have an infinite number of solutions to their system. /1

I can translate a word problem into two algebraic equations. /5

Academic Practice: Grade: /7

Summary: Day 2 (Tuesday, February 18, 2014)

Solving Systems of Equations Algebraically 1 - Substitution ☺ " Test

I can solve linear equations for a variable of my choice. N/A

I can solve systems of linear equations using the substitution method /6



Summary: Day 3 (Block Day, February 19-20, 2014)

Solving Systems of Equations Algebraically 2 - Elimination ☺ " Test

I can convert linear equations into a form of my choosing. N/A

I can solve systems of linear equations using the substitution method /6



Summary: Day 4 (Friday, February 21, 2014)

Solving Systems of Equations Algebraically 3 – Best Method ☺ " Test I can determine the most efficient method of solving for a system of equations. N/A


Academic Practice: Grade: /5 Summary:

Name:__________________________________________ Date:_____________________ Period:_____


Day 5 (Monday, February 24, 2014)

Systems of Linear Equations Review ☺ " Test

I can show mastery of the student expectations from Days 1-5. /12

Day 6 (Tuesday, February 25, 2014)

Unit 12 Test: Systems of Linear Equations Grade Test

I can show mastery of the student expectations from Days 1-5. /12

TABLE

x y1 y2 2 4 6 3 5 5 4 6 4 5 7 3

OR

x y 2 4 3 5 4 6 5 7

x y 2 6 3 5 4 4 5 3

GRAPHING

𝑦 = — 1𝑥 + 5 y = 𝑥 + 3

SUBSTITUTION

Ex 1. y = 𝑥 + 2 𝑥 + 𝑦 = 8

Ex 2. y = 𝑥 + 74𝑥 + 2𝑦 = 4

ELIMINATION

Ex 1. 3𝑥 + 3𝑦 = 34 3𝑥 − 3𝑦 = −4

Ex 2. −2𝑥 + 2𝑦 = 10 𝑥 + 𝑦 = −4

Solving Systems of Equations

Name:__________________________________________ Date:_____________________ Period:_____


DAY 1: SOLVING SYSTEMS OF EQUATIONS THROUGH GRAPHING AND TABLES

1. A system of linear equations is a set of 2 or more linear equations.

2. The solution of a system is an ______________________ that makes both equations __________.

3. On a graph of both equations, the solution is where the lines ________________________________.

4. Systems of equations can have one of the following:

One Solution

___________________________

No Solutions

__________________________

Infinitely Many Solutions

___________________________

To Solve a system of equations by graphing:

1. ______________ each line very carefully.

2. ______________ for where the lines intersect.

3. ______________ the solution in both equations.

I can graph a linear equation in slope intercept form. I can find the intersecting point of two lines and identify it as the solution of the system of equations.

*See pg. 384 of the textbook to see #5 & 6 worked out.

5. 𝑦 = 𝑥 − 3 𝑦 = −𝑥 − 1

Solution: ___________________

6. 𝑦 = −𝑥

𝑦 = − !!𝑥 + 1

Solution: ___________________

7. 𝑦 = 2

𝑦 = − !!𝑥 + 4

Solution: ___________________

Name:__________________________________________ Date:_____________________ Period:_____


I can recognize that parallel lines have no solution to their system. I can recognize that lines with the same slope and intercept have an infinite number of solutions to their system.

8. 𝑦 = −3𝑥 − 5𝑦 = −3𝑥

Solution: ___________________

9. 𝑦 = !

!𝑥 + 4

𝑦 = !!𝑥 + 1

Solution: __________________

10. 𝑦 = −3𝑥 + 6𝑦 = −3𝑥 + 6

Solution: ___________________

I can solve a linear equation in standard form for y to put it in slope intercept form.

11. 𝑦 = − !!𝑥 + 2

2𝑥 + 3𝑦 = 6

Solution: ___________________

12. −3𝑥 + 2𝑦 = −2𝑦 = −1𝑥 − 2

Solution: ___________________

Create a System of Equations that would result in each of the following:

13. One Solution

14. No Solution

15. Infinitely Many Solutions

Name:__________________________________________ Date:_____________________ Period:_____


Solving Systems of Linear Equations Using a Table

1. Make a table of values 2. Find an x-value that gives the same y-value for both equations. Ex. x y1 y2

2 4 6 3 5 5 4 6 4 5 7 3

OR

x y 2 6 3 5 4 4 5 3

*The solution is: ( , )

x y 2 4 3 5 4 6 5 7

The system can have:

One Solution

There is one x-value that gives the same y-value for both lines.

x y1 y2 0 -5 7 1 -4 4 2 -3 1 3 -2 -2

No Solution

There is no x-value that gives

the same y-value and slopes are the same.

x y1 y2 0 0 1 2 4 5 4 8 9 6 12 13

Infinitely Many Solutions

All x-values gives the same

y-values for both lines.

x y1 y2 0 0 0 2 4 4 4 8 8 6 12 12

Identify the solution and write as an ordered pair (x, y), no solution, or infinitely many solutions.

1. Solution:____________

x y1 y2 0 3 5 1 0 2 2 -3 -1 3 -6 -4

2. Solution:____________

x y1 y2 0 -6 6 1 -2 4 2 2 2 3 6 0

3. Solution:____________

x y1 y2 0 7 7 1 8 8 2 9 9 3 10 10

4. Solution:____________

x y1 y2 0 5 3 1 7 7 2 9 11 3 11 15

Identifying Solutions of Systems: Tell whether the ordered pair is a solution of the given system. *See pg. 383 of the textbook to see these worked out.

16. (4, 1); 𝑥 + 2𝑦 = 6𝑥 − 𝑦 = 3

17. (−1, 2); 2𝑥 + 5𝑦 = 83𝑥 − 2𝑦 = 5

18. (1, 3); 2𝑥 + 𝑦 = 5−2𝑥 + 𝑦 = 1

Name:__________________________________________ Date:_____________________ Period:_____


Introduction to Word Problems with Systems: What’s in My Pocket??? 1. I have nickels and dimes in my pocket that total 70 cents. How many do I have of each coin?

Your guess: ______________________________________________________________________

2. List all possible combinations that add to $0.70 in the table below with a partner:

Nickels (x)

Dimes (y)

Total Coins

3. Can you really know what I have in my pocket? What else would you need to know?

4. What if I told you I have a total of 11 coins? Would that determine the answer to what’s in my pocket? I can translate a word problem into two algebraic equations – Tables and Graphs.

*See pg. 385 of the textbook to see #1 worked out.

1. Bowl-o-Rama charges $2.50 per game plus $2 for shoe rental, and Bowling Pinz charges $2 per game plus $4 for shoe rental. For how many games will the cost to bowl be the same at both places? What is that cost?

Write a system of equations, one equation to represent the price at each company. Let x be the number of games played and y be the total cost.

Total Cost is price per game times games plus shoe rental.

Bowl-o-Rama

Bowling Pinz

• Graph both equations on your calculator (y1 = and y2 =) and view the graphs of the system. Where do

the two lines intersect? (Use the intersect feature of your calculator) What is the solution? _____ • Now look at the table on your calculator. Does this ordered pair appear for both equations? ________

2. To deliver mulch, Lawn and Garden charges $30 per cubic yard of mulch plus a $30 delivery fee. Yard

Depot charges $25 per cubic yard of mulch plus a $55 delivery fee. For how many cubic yards will the cost be the same? What will that cost be?

Total Cost is times plus

Lawn and Garden

Yard Depot

What is the solution? ___________________________________________________________________

Name:__________________________________________ Date:_____________________ Period:_____


DAY 2: SOLVING SYSTEMS OF EQUATIONS ALGEBRAICALLY – SUBSTITUTION

Make a Plan: Substitution works well when:

• One equation is already solved for one variable in terms of another like y = or x =

• One equation has a term with a coefficient of 1 or -1.

Make it Happen: • If necessary, solve one equation for one of

the variables. (Get x = or y = ) • Substitute the expression for the variable in

the other equation. • Solve the equation. You will almost always

have to distribute first. • Substitute your solution into either original

equation. • Solve for the remaining variable. • Write your answer as an ordered pair. • CHECK YOUR ANSWER IN BOTH EQUATIONS!

One Solution Ex:

No Solutions Ex:

Infinitely Many Solution Ex:

I can translate a word problem into two algebraic equations – Substitution. *See pg. 393 of the textbook to see #1 worked out.

1. One high-speed Internet provider has a $50 setup fee and costs $30 per month. Another provider has

no set-up fee and costs $40 per month. In how many months will both providers cost the same? What will that cost be?

System: ____________________ Solution (ordered pair): ______________ ____________________ Solution (words) __________________________________________

Name:__________________________________________ Date:_____________________ Period:_____


COLOR BY SOLUTION – USING SUBSTITUTION

Solve each system using Substitution. Find each answer and color with the given color.

1. y = 6x – 11 −2x − 3y = −7

Solution: ( , ) - Purple 2. 2x − 3y = −1

y = x − 1

3. y = −3x + 5

5x − 4y = −3

4. −3x − 3y = 3 5x + y = − 17

Solution: ( , ) – Light Blue

Solution: ( , ) - Yellow

5. y = −2 4x – 3y = 18

6. y = 5x − 7 −3x − 2y = −12

Solution: ( , ) – Lime

Solution: ( , ) – Teal

Solution: ( , ) - Blue

Name:__________________________________________ Date:_____________________ Period:_____


DAY 3: SOLVING SYSTEMS OF EQUATIONS ALGEBRAICALLY – ELIMINATION

Make a Plan: Elimination works well when

• No variable is already solved for • No coefficient is 1 or -1

Make it Happen: • GOAL – to create additive opposites (Ex. 4x, -

4x or -7y, 7y ) • If necessary, multiply one or both equations

by a constant to create additive opposites. • Add the two equations. This should eliminate

one of the variables. • Solve for the variable. • Substitute into either original equations and

solve for the remaining variable. • Write your answer as an ordered pair. • CHECK YOUR ANSWER IN BOTH EQUATIONS!

One Solution Ex:

No Solutions Ex:

Infinitely Many Solution Ex:

I can translate a word problem into two algebraic equations – Elimination. *See pg. 400 of the textbook to see #1 worked out.

1. Sam spent $24.75 to buy 12 flowers for his mother. The bouquet contained roses and daisies. How many of each type of flower did Sam buy?

System: ___________________ Solution (ordered pair): ______________ ___________________ Solution (words) ____________________

Name:__________________________________________ Date:_____________________ Period:_____


COLOR BY SOLUTION – USING ELIMINATION

Solve each system using Elimination. Find each answer and color with the given color.

7. −4x − 2y = −12

4x + 8y = −24

Solution: ( , ) - Magenta 8. 4x + 8y = 20 −4x + 2y = −30

9. x − y = 11

2x + y = 19

10. −6x + 5y = 1 6x + 4y = −10

Solution: ( , ) – Purple

Solution: ( , ) - Turquoise

11. −2x − 9y = −25 −4x − 9y = −23

12. 8x + y = −16 −3x + y = −5

Solution: ( , ) – Orange

Solution: ( , ) – Light Pink

Solution: ( , ) – Lime

Name:__________________________________________ Date:_____________________ Period:_____


UNIT 12: SYSTEMS OF LINEAR EQUATIONS OVERVIEW Solutions to Systems One Solution Infinitely Many No Solution

Graphically

(Using a Graph)

Algebraically

(Using substitution or elimination)

Tabular

(Using a Table)

Using Substitution to Solve Systems of Equations

Write the “Helpful Hint” on pg. 390: ____________________________________________________ ________________________________________________________________________________________________________________________________________________________________________ Using Elimination to Solve Systems of Equations

(p. 397, 1st paragraph): To do this you __________ the two equations in the system together. (p. 397, 2nd paragraph) To get a term to eliminate you must have _______________ coefficients. More Word Problems Practice

1. Angelo runs 7 miles per week and increases his distance by 1 mile each week. Marc runs 4 miles per week and increases his distance by 2 miles each week. In how many weeks will Angelo and Marc be running the same distance? What will that distance be?


2. The school band sells carnations on Valentine’s Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge.


Name:__________________________________________ Date:_____________________ Period:_____


ALGEBRA 1 – UNIT 12: SYSTEMS OF LINEAR EQUATIONS · ALGEBRA 1 – UNIT 12 · WEEK 7 · SYSTEMS OF LINEAR EQUATIONS NOTES & PRACTICE PAGE 5 Solving Systems of Linear Equations Using

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