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Secondary One Mathematics:
An Integrated Approach
Module 2 HonorsSystems
By
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
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Systems 2.1
© 2012 Mathematics Vision Project | M P
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.
1. 2.
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.
3. 4.
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5
Systems 5
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Systems 2.1
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
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.
Go
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.
6. 7.
8. 9.
Need help? Check out this related video:
https://www.youtube.com/watch?v=vo-CXaCf1I4
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Systems 6
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Systems 7
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Systems 8
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Systems 2.2
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
. f l i
r .
t
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)
Set
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.
6. 7.
8.
9.
9
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Name: Systems 2.2
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
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?
11.
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
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Name: Systems 2.3
© 2012 Mathematics Vision Project | M P
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: 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.
1. {
a. (-2 , 5)
b. (2 , 1)
c. (4 , 5)
2. {
a. (-1 , 0)
b. (6 , -3)
c. (0 , 3)
3. {
a. (7 , 2)
b. (2 , -14)
c. (-2 , 2)
4. {
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.
5. 6.
© 2012 www.flickr.com/photos/dugspr
13
Systems 13
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Name: Systems 2.3
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
7. 8.
Go
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.
13.
14.
15.
16.
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
9. 3
4+1
810.
3
5+
7
1011.
2
3+1
412.
4
7+
8
21
14
Systems 14
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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15
Systems 15
8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 23/88
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 24/88
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 25/88
Name: Systems 2.4
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Ready, Set, Go!
Ready
Topic: Substitution and Solving Equations
Determine whether is a solution to each problem.
1. ( )
2. ( )
3.
4.
5.
Determine the value of x that makes each equation true.
6. 7. ( ) 8.
Set
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?
© 2012 www.flickr.com/photos/loungerie
16
Systems 16
8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 26/88
Name: Systems 2.4
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Go
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
d
16. Ffor)32(9
5 F C
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
17
Systems 17
8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 27/88
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18
Systems 18
8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 28/88
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Name: Systems 2.5
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Ready, Set, Go!
Ready
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.
1.1
5 x 4 2. 3 x+5
3. 5 x 2 y 10 4. 3 x+4 y ³ 24
© 2012 www.flickr.com/photos//dugspr
19
Systems 19
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Name: Systems 2.5
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Set
Topic: Writing two variable inequalities
Given the graph with the regions that are shaded write the inequality or system of
inequalities.
5. 6.
7. 8.
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
20
Systems 20
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Name: Systems 2.5
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Go
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
Table
Days Cost123
4
81624
32
Create a context
10. Equation: Graph Table
Create a context
Claire earns $9 per week allowance.
21
Systems 21
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Name: Systems 2.5
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
11. Equation: y = 3 x Graph
Table
Create a context
12. Equation: Graph
Table
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
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 39/88
Name: Systems 2.6
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
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:
Set
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?
© 2012 www.flickr.com/photos/photosteve101
24
Systems 24
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Systems 2.6
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Go
Topic: Graph two variable inequalities
Graph the following inequalities.
10. 11. 12.
13. 14. 15.
Need help? Check out these related videos.
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
25
Systems 25
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Systems 2.7
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
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.
Set
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?
© 2012 www.flickr.com/photos/tudor
27
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Name: Systems 2.7
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Go
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
12.
13.
Solve each inequality. Give the solution in inequality notation and set notation.
14.
15.
16.
17.
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/
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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1
3 x+
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Systems 2.8
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Ready, Set, Go!
Ready
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).
5. 6.
Set
Topic: Solve systems of equations
Solve the following systems of equations using elimination of variables, then justify
graphically.
7. { 8. {
9.
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?
-5
-5
5
5
-5
-5
5
5
© 2012 www.flickr.com/photos/gwilmore
-5
-5
5
5
30
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Name: Systems 2.8
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Go
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.
Need help? Check out these related videos.
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
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Name: Systems 2.9
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Ready, Set, Go!
Ready
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.
Set
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.
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8
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© 2012 www.flickr.com/photos/msciba
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Name: Systems 2.9
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Go
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. {
Need help? Check out these related videos.
http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/graphing-systems-of-inequalities-2
-10
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Systems 37
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Systems 38
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Systems 41
8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Systems 2.12
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Ready, Set, Go!
Ready
Topic: Solve exponential equations
Find the value of x for each situation.
1. 2. 3. 4.
Set
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.
Go
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.
t
t
l
Pounds of Fruit Salad
10
10
© 2012 www.flickr.com/photos/dugspr
-5
-5
5
5
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Name: Systems 2.12
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Graph each set of inequalities and determine the solution region.
7. { 8. {
9. 10.
Need help? Check out these related videos.
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
44
Systems 44
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Systems 46
8/13/2019 Sec1 Mod2 Systems Tnh 71713
http://slidepdf.com/reader/full/sec1-mod2-systems-tnh-71713 76/88
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: To Market with Matrices 2.13H
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Ready, Set, Go!
Ready
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
3 x
4 y
14
5. x 2 y 11
x 4
y 2
6.2 x y 0
5 x
3 y
1
2 0 1 2
. f l i c k r
. c o
/ p h o t o s / t o
y h j /
47
Systems 47
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Name: To Market with Matrices 2.13H
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Set
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 { [ | ]
48
Systems 48
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Name: To Market with Matrices 2.13H
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Go
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
y x 4
10. y 2 x 7
3 x y 8
11.4 x y 7
3 x 2 y 8
Need help? Check out these related videos:
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
49
Systems 49
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8/13/2019 Sec1 Mod2 Systems Tnh 71713
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Name: Solving Systems with Matrices 2.14H
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license
Ready, Set, Go!
Ready
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.
Set
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. [ | ]
5.
[ |
]
2012 www.flickr.com/photos/dansmath
52
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Name: Solving Systems with Matrices 2.14H
Go
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
Need help? Check out these related videos:
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
53