Sec1 Mod2 Systems Tnh 71713

8/13/2019 Sec1 Mod2 Systems Tnh 71713

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Secondary One Mathematics:

An Integrated Approach

Module 2 HonorsSystems

The Mathematics Vision Project:

Scott Hendrickson, Joleigh Honey,

Barbara Kuehl, Travis Lemon, Janet Sutoriuswww.mathematicsvisionproject.org

In partnership with the

Utah State Office of Education

Systems 1

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Systems 2

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Name: Systems 2.1

In partnership with the Utah State Office of Education

Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license

Ready, Set, Go!

ReadyTopic: Determine if given value is a solution and solve systems of equations

Substitute the given points into the equations to determine which ordered pair satisfies the

system of linear equations, then graph both equations and label the point of intersection.

a. () a. (2, 7)

b. ( ) b. (-7, 11)

c. ( ) c. (0, 5)

Solve the following systems by graphing. Check the solution by evaluating both equations atthe point of intersection.

Systems 5

Name: Systems 2.1

Set Topic: Determining possible solutions

5. A theater wants to take in at least $2000 for a certain matinee. Children’s tickets cost $5 each and

adult tickets cost $10 each. The theater can seat up to 350 people. Find five combinations ofchildren and adult tickets that will make their goal.

Topic: graphing linear equations and determining if a given value is a solution

Graph each equation below, then determine if the point (3,5) is a solution to the equation.

Name two additional points that are solutions to the equation and show these points on the

graph.

Need help? Check out this related video:

https://www.youtube.com/watch?v=vo-CXaCf1I4

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Name: Systems 2.2

In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license

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Ready, Set, Go!

ReadyTopic: Determining if given values are solutions to an equation

Identify which of the given points are solutions to the following linear equations.

1. 3x + 2y = 12 2. 5x – y = 10

a. (2, 4) a. (2, 0)

b. (3, 2) b. (3, 0)

c. (4, 0) c. (0, -10)

d. (0, 6) d. (1, 1)

Find the value that will make each ordered pair a solution to the given equations.

3. x + y = 6 4. 2x + 4y = 8 5. 3x – y = 8

a. (2, __) a. (2, __) a. (2, __)

b. (0, __) b. (0, __) b. (0, __)

c. (__, 0) c. (__, 0) c. (__, 0)

Topic: Graph linear inequalities

Graph the following inequalities on the coordinate plane. Name one point that is a solution

to the inequality and one point that is not a solution. Show algebraically and graphically that

your points are correct.

Systems 9

Name: Systems 2.2

Go Topic: Solving inequalities

Follow the directions for each problem below. (Show your work!)

10. a. Solve for x. Then graph the solution on the number line.

b. Select an x-value from your graph of the solution of the inequality. Replace x in the original

inequality with your chosen value. Does the inequality hold true?

c. Select an x-value that is outside of the solution set on your graph. Replace x in the original

inequality with your chosen value. Does the inequality still hold true?

a. Solve for y.

b. Now imagine that your inequality is an equation. In other words, your solution will say y = ,

instead of y > or y <. With the equal sign, it should be the equation of a line. Graph your equation.

c. Find the y – intercept.

d. Find the slope.

e. Select a point that is above the line. ( , )

Replace the x and y–

values in the inequality

Is the inequality still true?

f. Select a point that is below the line. ( , )

Replace the x and y – values in the inequality

Is the inequality still true?

g. Explain which side of the line should be shaded.

h. Decide whether the line should be solid or dotted. Justify your decision.

Need help? Check out these related videos:

http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/graphing-linear-inequalities-in-two-variables-2

Systems 10

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Name: Systems 2.3

Ready, Set, Go!

ReadyTopic: Determining points that satisfy equations and solving systems of equations

Three points are given. Each point is a solution to at least one of the equations. Find the

point that satisfies both equations. (This is the solution to the system!) Justify that the point

is a solution to both equations and that the others are not.

a. (-2 , 5)

b. (2 , 1)

c. (4 , 5)

a. (-1 , 0)

b. (6 , -3)

c. (0 , 3)

a. (7 , 2)

b. (2 , -14)

c. (-2 , 2)

a. (1 , 6)

b. (-3 , -2)

c. (-3 , 2)

SetTopic: Graphing linear equations from standard form using intercepts

Graph the following equations by finding the intercepts.

Systems 13

Name: Systems 2.3

Topic: Adding and multiplying fractions

Add. Reduce your answers but leave as improper fractions when applicable.

Multiply. Reduce your answers but leave as improper fractions when applicable.

Need help? Check out these video lessons.

http://www.youtube.com/watch?v=cuNpXve18Pc

http://www.youtube.com/watch?v=6zixwWZ88tk

http://www.youtube.com/watch?v=oHNR0FK_lDE

Systems 14

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Systems 15

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Name: Systems 2.4

Ready, Set, Go!

Topic: Substitution and Solving Equations

Determine whether is a solution to each problem.

1. ( )

2. ( )

Determine the value of x that makes each equation true.

6. 7. ( ) 8.

Topic: Creating equations, solving real world problems, solve systems of equations

A phone company offers a choice of three text-messaging plans. Plan A gives you unlimited text

messages for $10 a month; Plan B gives you 60 text messages for $5 a month and then charges you

$0.05 for each additional message; and Plan C has no monthly fee but charges you $0.10 per

message.

9. Write an equation for the monthly cost of each of the three plans.

10. If you send 30 messages per month, which plan is cheapest?

11. What is the cost of each of the three plans if you send 50 messages per month?

12. Determine the values for which each plan is the cheapest?

Systems 16

Name: Systems 2.4

Topic: Solve literal equations

Re-write each of the following equations for the indicated variable.

13. 3 x + 5y = 30 for y 14. 24 x + 6y = 360 for x

15. dfor32

801280c

16. Ffor)32(9

17. =mx+b for b 18. x+ By=C for y

Need help? Check out these related videos.

What does it mean to be a solution?http://patrickjmt.com/an-intro-to-solving-linear-equations-what-does-it-mean-to-be-a-solution/

http://patrickjmt.com/solving-linear-equations/

Solving for a variable.

http://www.khanacademy.org/math/algebra/solving-linear-equations/v/solving-for-a-variable

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Systems 18

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Name: Systems 2.5

Ready, Set, Go!

Topic: Graphing two variable inequalities

For each inequality and graph, pick a point and use it to determine which half-plane should

be shaded, then shade the correct half-plane.

5 x 4 2. 3 x+5

3. 5 x 2 y 10 4. 3 x+4 y ³ 24

Systems 19

Name: Systems 2.5

Topic: Writing two variable inequalities

Given the graph with the regions that are shaded write the inequality or system of

inequalities.

Systems 20

Name: Systems 2.5

Topic: Proportional relationships

For each proportional relationship below, one representation is provided. Show the

remaining representations and explain any connections you notice between

representations.

9. Equation: Graph

Days Cost123

Create a context

10. Equation: Graph Table

Create a context

Claire earns $9 per week allowance.

Systems 21

Name: Systems 2.5

11. Equation: y = 3 x Graph

Create a context

12. Equation: Graph

Days Cost

Create a context

Need Help? Check out these related videos.

http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/graphing-linear-inequalities-in-two-variables-3

Systems 22

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Name: Systems 2.6

Ready, Set, Go! Ready

Topic: Determine patterns

Find the next two values in the pattern. Describe how you determined these values.

1. 3, 6, 9, 12, ____, ____ Description:

2. 3, 6, 12, 24, ____, ___ Description:

3. 24, 20, 16, 12, ___, ___ Description:

4. 24, 12, 6, 3, ___, ___ Description:

Topic: Solve systems of equations using substitution

For questions 5-8 solve the system of equations using substitution. Check your work by

graphing.

5. { 6. {

7. { 8. {

9. Tickets to a show cost $10 in advance and $15 at the door. If 120 tickets are sold for a total of$1390, how many of the tickets were bought in advance?

Systems 24

Name: Systems 2.6

Topic: Graph two variable inequalities

Graph the following inequalities.

10. 11. 12.

13. 14. 15.

http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/solving-systems-by-substitution-3

http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/solving-and-graphing-linear-inequalities-in-two-

variables-1

http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/graphing-inequalities-2

Systems 25

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Systems 26

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Name: Systems 2.7

Ready, Set, Go!

ReadyTopic: Exponents

Write the following in exponential notation.

1. 4 × 4 × 4 × 4 × 4 2.

Find each value.

3. 4. 5. 6. 7.

Topic: Solving systems

8. Nadia and Peter visit the candy store. Nadia buys three candy bars and four fruit roll-ups for$2.84. Peter also buys three candy bars, but can only afford one additional fruit roll-up. Hispurchase costs $1.79. What is the cost of a candy bar and a fruit roll-up individually?

9. A farmer noticed that his chickens were loose and were running around with the cows in the cowpen. He quickly counted 100 heads and 270 legs. How many chickens did he have and how manycows?

Systems 27

Name: Systems 2.7

Topic: Solve one variable inequalities.

Solve the following inequalities. Write the solution set in interval notation and graph the

solution set on a number line.

10. 4 x + 10 < 2 x + 14

11. 2 x + 6 > 55 – 5 x

Solve each inequality. Give the solution in inequality notation and set notation.

18. 19.

Need help? Check out these related videos?

Exponential notation:

http://www.khanacademy.org/math/algebra/exponents-radicals/v/understanding-exponents

Solving inequalities:http://www.khanacademy.org/math/algebra/solving-linear-inequalities/v/solving-inequalities

http://www.khanacademy.org/math/algebra/solving-linear-inequalities/v/multi-step-inequalities-2

Set notation and interval notation:

http://patrickjmt.com/using-interval-notation-to-express-inequalities-ex1/

Systems 28

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24 x + 6 y = 360

15 y= 8

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24 x + 6 y = 360

5 x + 4 y = 120

F)*1 +?L(,7LM ()* (07 *U?'(,01 OM c '1> ()* O0((0+ *U?'(,01 OM e (0 I*( ()* ) f-0*<<,-,*1( ()* .'+*

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30 x + 24 y = 720

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=40P1*: ?*#:)G 9*%G O,D 9)(%*+( 2>Q

Name: Systems 2.8

Ready, Set, Go!

Topic: Evaluate exponents

Simplify and evaluate the following.

1. 3-2 2. (0.5)-2 3. 24 4. 4-2

Write the following expression three different ways (one way can include the simplified value).

Topic: Solve systems of equations

Solve the following systems of equations using elimination of variables, then justify

graphically.

7. { 8. {

10. A 150-yard pipe is cut to provide drainagefor two fields. If the length of one piece (a) isthree yards less than twice the length of thesecond piece (b), what are the lengths of the twopieces?

Systems 30

Name: Systems 2.8

Topic: Graph two variable linear inequalities

Graph the following linear inequalities on the graphs below. Include constraints.

11. Ben has enough money to buy up to eight yogurts. If hisfavorite flavors are blueberry and strawberry, what are all

the possible combinations he can buy? Graph the inequality

that shows all possible combinations of his favorite flavors.

12. Peggy is buying a balloon bouquet. Her favorite colors

are silver and purple. The silver balloons are $1 and the

purple balloons are $0.80. Graph an inequality that shows

how many of each color balloon she can put in her bouquet if

she doesn’t spend more than $20.

Negative exponentshttp://patrickjmt.com/negative-exponents/ http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/zero--negative--and-fractional-exponents

Solving systems by elimination

http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/solving-systems-by-elimination-2

Solving systems by graphing

http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/solving-linear-systems-by-graphing

Blueberry

S t r a w b e r r y

Silver

P u r p l e

Systems 31

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Systems 32

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Name: Systems 2.9

Ready, Set, Go!

Topic: Solving two variable inequalities

1. A theater wants to take in at least $2000 for a certain matinee. Children’s tickets cost $5 eachand adult tickets cost $10 each.

a. Write an inequality describing the number of tickets that will allow the theater to meet theirgoal of $2000.

b. If the theater has a maximum of 350 seats, write an inequality describing the number of both

types of tickets the theater can sell.

c. Find the number of children and adult tickets that can be sold so that all seats are sold and the$2000 goal is reached.

Topic: Writing equations of two variable inequalities

Given the graph with the regions that are shaded write the inequality or system of

inequalities.

2. 3. 4.

Systems 33

Name: Systems 2.9

Topic: Graph two variable inequalities

Graph each set of inequalities below. Include the shaded region of both, plus indicate the

region that is true for all inequalities.

5. { 6. {

Solve the following systems of equations.

7. Nadia and Peter visit the candy store. Nadia buys three candy bars and four fruit roll-ups for$2.84. Peter also buys three candy bars, but can only afford one additional fruit roll-up. Hispurchase costs $1.79. What is the cost of a candy bar and a fruit roll-up individually?

8. { 9. {

http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/graphing-systems-of-inequalities-2

Systems 34

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6 " # 8 * : # 0 1 C = , 0 + 0 & C 1 0 1 1 . / $ %

Systems 35

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61 ()* <,1'G 7'3( 0< ()* ('.B .(?>*1(. *D(*1> ()* .(3'(*FK <03 .0GM,1F ' .K.(*+ 0< G,1*'3 *L?'(,01. (0 '.,(?'(,01 ()'( -01(',1. ()3** *L?'(,01. '1> ()3** ?1B1081.@ A),. 803B 730M,>*. '>>,(,01'G73'-(,-* 8,() ()* -01-*7(?'G ,>*'. 0< .0GM,1F ' G,1*'3 .K.(*+ 0< *L?'(,01.@

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n + 3 p + 2m = 7.50

2n + 6 p + 5m = 15.50

n + 2 p + 2m = 6.25

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Systems 37

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Systems 38

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Systems 39

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Systems 40

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Systems 41

! #$%# &'()*+'(,-. /,.,01 2304*-( 5 &! 2

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C'3D0. '1> CD'3,(' )'B* .?--*..<?DDE <0?1> ' 8'E (0 3*73*.*1( /&& 0<

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Systems 42

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Name: Systems 2.12

Ready, Set, Go!

Topic: Solve exponential equations

Find the value of x for each situation.

1. 2. 3. 4.

Topic: Create and solve two variable inequalities

5. Jane is buying fruit salad and potato salad for a picnic. Fruit salad costs $2.00 per pound and

potato salad costs $4.00 per pound. Jane needs to buy at least 6 pounds of salads and she doesn’t

want to spend more than $20. Write and graph a system of linear inequalities. Also, list 2 possible

combinations of salad Jane could buy.

Let x = pounds of fruit salad and

y = pounds of potato salad.

Topic: Find the solution region of the following systems of

inequalities.

6. Write the system of inequalities that is represented in thegraph to the right.

Pounds of Fruit Salad

Systems 43

Name: Systems 2.12

Graph each set of inequalities and determine the solution region.

7. { 8. {

9. 10.

Exponents http://patrickjmt.com/exponents-intro-to-evaluating-a-few-truefalse-questions/

Rules for exponents http://patrickjmt.com/basic-exponent-properties/

Solving a system of inequalities http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/systems-of-linear-inequalities

Systems 44

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87FJ.(/ 6(-/KL +(,L D&5 +K',(C' I9GM4

Name: To Market with Matrices 2.13H

Ready, Set, Go!

Topic: Solving Systems by Substitution and Elimination

Solve each system of equations using any algebraic method.

1.3 x y 1

3 x 2 y 16

2. x 2 y 5

3 x 5 y 14

3.4 x 2 y 8

x 2 y 7

4.2 x 3 y 2

5. x 2 y 11

6.2 x y 0

2 0 1 2

. f l i c k r

/ p h o t o s / t o

y h j /

Systems 47

Topic: Row reductions in Matrices

7. Create a matrix to match each step in the solving of the system of equations given. Also, write a

description of what happened to the equation and the matrix between steps.

System of Equations Description Matrix

Given System { [

Step 1 { [

Step 2 { [ | ]

Step 3 { [ | ]

Step 4 { [ | ]

Step 5 { [ | ]

Systems 48

Topic: Solving Systems of Equations by Graphing

Solve each system of equations by graphing.

8. y 3 x 3

y 3 x 3

9. y 4 x 1

10. y 2 x 7

3 x y 8

11.4 x y 7

3 x 2 y 8

http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/solving-linear-systems-by-substitution

http://patrickjmt.com/row-reducing-a-linear-system-of-equations/

http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/graphings-systems-of-equations

Systems 49

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Systems 50

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Systems 51

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87FG.(/ 6(-/HI +(,I D&5 +H',(C' J9KL4

Name: Solving Systems with Matrices 2.14H

Ready, Set, Go!

Topic: Solving systems of equations using matrices.

1. In an earlier assignment you worked the following

problem:

“ A theater wants to take in $2000 for a certain matinee. Children’s tickets cost $5 each and

adult tickets cost $10 each. If the theater has a maximum of 350 seats, write a system of

equations that can be solved to determine the number of both children and adult tickets the

theater can sell .”

Set up a matrix that goes with the situation described above.

Assume that the matrices below represent linear systems of equations. Practice the strategy

you used for reducing a given matrix so that the left portion of the matrix (the 2 rows and

first 2 columns of entries) has ones on the diagonal. Write a description of what you did to

get from one matrix to another in each step of your sequence of matrices.

2. [ | ] [

|] [ |]

3. [ |] [

4. [ | ]

2012 www.flickr.com/photos/dansmath

Systems 52

Name: Solving Systems with Matrices 2.14H

Topic: Solving systems of equations

Solve the following systems of equations with a method of your choice.

6. x y 11

2 x y 19

7.8 x y 16

3 x y 5

8.4 x 9 y 9

x 3 y 6

9.7 x y 19

2 x 3 y 19

http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/solving-linear-systems-by-graphing

http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/solving-linear-systems-by-substitution

Sec1 Mod2 Systems Tnh 71713

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