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Elementary Algebra

Chapter 5

Elementary AlgebraChapter 5
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope–Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solve Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Quadratic Trinomials with Leading Coefficient 1
    4. 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

Be Prepared

Try It

5.1

yes no

5.2

no yes

5.3

(3,2)(3,2)

5.4

(2,3)(2,3)

5.5

(−2,−2)(−2,−2)

5.6

(1,6)(1,6)

5.7

(3,4)(3,4)

5.8

(5,−4)(5,−4)

5.9

(4,2)(4,2)

5.10

(5,−3)(5,−3)

5.11

(9,−1)(9,−1)

5.12

(4,−6)(4,−6)

5.13

no solution

5.14

no solution

5.15

infinitely many solutions

5.16

infinitely many solutions

5.17

no solution, inconsistent, independent

5.18

no solution, inconsistent, independent

5.19

one solution, consistent, independent

5.20

one solution, consistent, independent

5.21

infinitely many solutions, consistent, dependent

5.22

infinitely many solutions, consistent, dependent

5.23

Manny needs 3 quarts juice concentrate and 9 quarts water.

5.24

Alisha needs 15 ounces of coffee and 3 ounces of milk.

5.25

(6,1)(6,1)

5.26

(4,2)(4,2)

5.27

(2,4)(2,4)

5.28

(−1,−3)(−1,−3)

5.29

(1,−2)(1,−2)

5.30

(2,6)(2,6)

5.31

(−2,−3)(−2,−3)

5.32

(6,2)(6,2)

5.33

(6,2)(6,2)

5.34

(8,2)(8,2)

5.35

(2,32)(2,32)

5.36

(12,−2)(12,−2)

5.37

infinitely many solutions

5.38

infinitely many solutions

5.39

no solution

5.40

no solution

5.41

The numbers are 3 and 7.

5.42

The numbers are 2 and −8.

5.43

The length is 12 and the width is 8.

5.44

The length is 23 and the width is 6.

5.45

The measure of the angles are 22 degrees and 68 degrees.

5.46

The measure of the angles are 36 degrees and 54 degrees.

5.47

There would need to be 160 policies sold to make the total pay the same.

5.48

Kenneth would need to sell 1,000 suits.

5.49

(2,−1)(2,−1)

5.50

(−2,3)(−2,3)

5.51

(3,−1)(3,−1)

5.52

(−2,5)(−2,5)

5.53

(1,1)(1,1)

5.54

(−2,4)(−2,4)

5.55

(1,3)(1,3)

5.56

(4,−3)(4,−3)

5.57

(6,2)(6,2)

5.58

(1,−2)(1,−2)

5.59

infinitely many solutions

5.60

infinitely many solutions

5.61

no solution

5.62

no solution

5.63

The numbers are 25 and 17.

5.64

The numbers are −25 and 10.

5.65

The bag of diapers costs $11 and the can of formula costs $13.

5.66

There are 105 calories in a banana and 5 calories in a strawberry.

5.67

Since both equations are in standard form, using elimination will be most convenient. Since one equation is already solved for xx, using substitution will be most convenient.

5.68

Since one equation is already solved for yy, using substitution will be most convenient; Since both equations are in standard form, using elimination will be most convenient.

5.69

{m+n=−23m=n7{m+n=−23m=n7

5.70

{m+n=−18m=n+40{m+n=−18m=n+40

5.71

{w+h=84,000h=2w18,000{w+h=84,000h=2w18,000

5.72

{s=2n5s+n=43{s=2n5s+n=43

5.73

Ali is 28 and Jameela is 16.

5.74

Jake is 9 and his dad is 33.

5.75

Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.

5.76

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

5.77

The angle measures are 55 degrees and 35 degrees.

5.78

The angle measures are 5 degrees and 85 degrees.

5.79

The angle measures are 42 degrees and 138 degrees.

5.80

The angle measures are 66 degrees and 114 degrees.

5.81

The length is 60 feet and the width is 35 feet.

5.82

The length is 60 feet and the width is 38 feet.

5.83

It will take Clark 4 hours to catch Mitchell.

5.84

It will take Sally 112112 hours to catch up to Charlie.

5.85

The rate of the boat is 11 mph and the rate of the current is 1 mph.

5.86

The speed of the canoe is 7 mph and the speed of the current is 1 mph.

5.87

The speed of the jet is 235 mph and the speed of the wind is 30 mph.

5.88

The speed of the jet is 408 mph and the speed of the wind is 24 mph.

5.89

There were 206 adult tickets sold and 347 children tickets sold.

5.90

There were 521 adult tickets sold and 842 children tickets sold.

5.91

Matilda has 13 dimes and 29 quarters.

5.92

Juan has 36 nickels and 63 dimes.

5.93

Greta should use 3 pounds of peanuts and 2 pounds of cashews.

5.94

Sammy should purchase 10 pounds of beans and 10 pounds of ground beef.

5.95

LeBron needs 120 ml of the 25% solution and 30 ml of the 50% solution.

5.96

Anatole should mix 125 ml of the 10% solution and 125 ml of the 40% solution.

5.97

Leon should put $42,000 in the stock fund and $8000 in the savings account.

5.98

Julius invested $1,750 at 11% and $5,250 at 13%.

5.99

The principal amount for the bank loan was $4,000. The principal amount for the federal loan was $14,000.

5.100

The principal amount for was $41,200 at 4.5%. The principal amount was, $24,000 at 7.2%.

5.101

no yes

5.102

no no

5.109

no solution

This figure shows a graph on an x y-coordinate plane of 3x – 2y is less than or equal 12 and y is greater than or equal to (3/2)x + 1. The area to the left or right of each line is shaded different colors. There is not overlapping area.
5.110

no solution

This figure shows a graph on an x y-coordinate plane of x + 3y is greater than 8 and y is less than –(1/3)x – 2. The area to the above or below each line is shaded slightly different colors. There is no overlapping area. Both lines are dotted.
5.111

y3x+1y3x+1

This figure shows a graph on an x y-coordinate plane of y is greater than or equal to 3x + 1 and -3x + y is greater than or equal to -4. The area to the left of each line is shaded with the overlapping area shaded a slightly different color.
5.112

x+4y4x+4y4

This figure shows a graph on an x y-coordinate plane of y is less than or equal to –(1/4)x + 2 and x + 4y is less than or equal to 4. The area to the below each line is shaded with the overlapping area shaded a slightly different color.
5.113
  1. {30m+20p1602m+3p15{30m+20p1602m+3p15

  2. This figure shows a graph on an x y-coordinate plane of 30m + 20p is less than or equal 160 and 2m + 3p is less than or equal to 15. The area to the left of each line is shaded with the overlapping area shaded a slightly different color.
  3. yes
  4. no
5.114
  1. {ap+5a+2p400{ap+5a+2p400

  2. This figure shows a graph on an x y-coordinate plane of a is greater than or equal to p + 5 and a + 2p is less than or equal to 400. The area to the left of each line is shaded different colors with the overlapping area also shaded a different color.
  3. no
  4. no
5.115
  1. {0.75d+2e25360d+110e1000{0.75d+2e25360d+110e1000

  2. This figure shows a graph on an x y-coordinate plane of 0.75d + 2e is less than or equal to 25 and 360d + 110e is greater than or equal to 1000. The area to the left or right of each line is shaded slightly different colors with the overlapping area also shaded a slightly different color.
  3. yes
  4. no
5.116
  1. {140p+125j10001.80p+1.25j12{140p+125j10001.80p+1.25j12

  2. This figure shows a graph on an x y-coordinate plane of 140p + 125j is greater than or equal to 1000 and 1.80p + 1.25j is less than or equal to 12. The area to the left or right of each line is shaded slightly different colors with the overlapping area also shaded a slightly different color.
  3. yes
  4. no

Section 5.1 Exercises

1.

yes no

3.

yes no

5.

yes no

7.

no yes

9.

(−2,3)(−2,3)

11.

(1,2)(1,2)

13.

(0,2)(0,2)

15.

(2,4)(2,4)

17.

(2,−1)(2,−1)

19.

(1,2)(1,2)

21.

(3,2)(3,2)

23.

(1,1)(1,1)

25.

(−1,−4)(−1,−4)

27.

(3,3)(3,3)

29.

(−5,6)(−5,6)

31.

(6,−2)(6,−2)

33.

(3,2)(3,2)

35.

(1,3)(1,3)

37.

(−3,1)(−3,1)

39.

no solution

41.

no solution

43.

no solution

45.

infinitely many solutions

47.

infinitely many solutions

49.

(2,2)(2,2)

51.

0 solutions

53.

0 solutions

55.

no solutions, inconsistent, independent

57.

consistent, 1 solution

59.

infinitely many solutions

61.

infinitely many solutions

63.

Molly needs 16 ounces of strawberry juice and 48 ounces of water.

65.

Enrique needs 8 ounces of nuts and 16 ounces of water.

67.

Leo should plant 50 tulips and 300 daffodils.

69.

Given that it is only known that the slopes of both linear equations are the same, there are either no solutions (the graphs of the equations are parallel) or infinitely many.

Section 5.2 Exercises

71.

(−2,0)(−2,0)

73.

(7,6)(7,6)

75.

(0,3)(0,3)

77.

(6,−3)(6,−3)

79.

(3,−1)(3,−1)

81.

(6,6)(6,6)

83.

(5,0)(5,0)

85.

(−2,7)(−2,7)

87.

(−5,2)(−5,2)

89.

(−1,7)(−1,7)

91.

(−3,5)(−3,5)

93.

(10, 12)

95.

(12,3)(12,3)

97.

(12,34)(12,34)

99.

Infinitely many solutions

101.

Infinitely many solutions

103.

No solution

105.

No solution

107.

The numbers are 6 and 9.

109.

The numbers are −7 and −19.

111.

The length is 20 and the width is 10.

113.

The length is 34 and the width is 8.

115.

The measures are 16° and 74°.

117.

The measures are 45° and 45°.

119.

80 cable packages would need to be sold.

121.

Mitchell would need to sell 120 stoves.

123.

t=2t=2 hours s=212s=212 hours

125.

Answers will vary.

Section 5.3 Exercises

127.

(6, 9)

129.

(−2,1)(−2,1)

131.

(−7,−1)(−7,−1)

133.

(−2,−4)(−2,−4)

135.

(−1,3)(−1,3)

137.

(−1,2)(−1,2)

139.

(−5,9)(−5,9)

141.

(6, 1)

143.

(−2,10)(−2,10)

145.

(2, 3)

147.

(−7,6)(−7,6)

149.

(−9,3)(−9,3)

151.

(9, 5)

153.

(−3,2)(−3,2)

155.

(−2,3)(−2,3)

157.

infinitely many solutions

159.

infinitely many solutions

161.

infinitely many solutions

163.

inconsistent, no solution

165.

inconsistent, no solution

167.

The numbers are 20 and 45.

169.

The numbers are 16 and −43.

171.

A shirt costs $16 and a sweater costs $33.

173.

There are 860 mg in a hot dog. There are 1,000 mg in a cup of cottage cheese.

175.

elimination substitution

177.

substitution elimination

179.

r=4r=4 c=1c=1

181.
  1. (8, 2)

  2. This image is a graph that shows the solution to the system “x plus y equals 10” and 5x plus 8y equals 56. The solution is on an x, y coordinate plane. Two arrows intersect at points 8 and 2.
  3. Answers will vary.

Section 5.4 Exercises

183.

The numbers are 6 and 9.

185.

The numbers are −5 and −25.

187.

The numbers are 5 and 4.

189.

The numbers are 2 and 3.

191.

$10,000

193.

She put $15,000 into a CD and $35,000 in bonds.

195.

The amount of the first year’s loan was $30,000 and the amount of the second year’s loan was $12,000.

197.

Bethany is 16 years old and Alyssa is 28 years old.

199.

Noelle is 20 years old and her dad is 54 years old.

201.

The small container holds 20 gallons and the large container holds 30 gallons.

203.

There were 10 calories burned jogging and 10 calories burned cycling.

205.

Notebooks are $4 and thumb drives are $20.

207.

The measures are 60 degrees and 30 degrees.

209.

The measures are 125 degrees and 55 degrees.

211.

94 degrees and 86 degrees

213.

72.5 degrees and 17.5 degrees

215.

The measures are 44 degrees and 136 degrees.

217.

The measures are 34 degrees and 56 degrees.

219.

The width is 10 feet and the length is 25 feet.

221.

The width is 15 feet and the length is 15 feet.

223.

It took Sarah’s sister 12 hours.

225.

It took Lucy’s friend 2 hours.

227.

The canoe rate is 5 mph and the current rate is 1 mph.

229.

The boat rate is 6.5 mph and the current rate is 2.5 mph.

231.

The jet rate is 240 mph and the wind speed is 28 mph.

233.

The jet rate is 415 mph and the wind speed is 19 mph.

235.

s=183,a=242s=183,a=242

237.

Answers will vary.

Section 5.5 Exercises

239.

There 1120 adult tickets and 530 child tickets sold.

241.

Josie bought 40 adult tickets and 32 children tickets.

243.

There were 125 adult tickets and 128 children tickets sold.

245.

Brandon has 12 quarters and 8 dimes.

247.

Peter had 11 dimes and 48 quarters.

249.

The cashier has fourteen $10 bills and sixteen $20 bills.

251.

Marissa should use 60 pounds of the $1.20/lb candy and 30 pounds of the $1.80/lb candy.

253.

Hannah needs 10 gallons of soda and 15 gallons of fruit drink.

255.

Julia and her husband should buy 12 pounds of City Roast Columbian coffee and 8 pounds of French Roast Columbian coffee.

257.

Jotham should mix 2 liters of the 30% solution and 28 liters of the 80% solution.

259.

The scientist should mix 15 liters of the 25% solution and 50 liters of the 12% solution.

261.

160 liters of the 40% solution and 80 liters of the 70% solution will be used.

263.

Hattie should invest $900 at 12% and $2,100 at 10%.

265.

Sam invested $28,000 at 10% and $20,000 at 6%.

267.

The federal loan is $62,500 and the bank loan is $3,300.

269.

$12,000 should be invested at 5.25% and $13,000 should be invested at 4%.

271.

14 boys paid the full-year fee. 4 boys paid the partial-year fee,

273.

Answers will vary.

Section 5.6 Exercises

275.

true false

277.

false true

279.

true false

281.

true true

283.
This figure shows a graph on an x y-coordinate plane of y is less than or equal to 3x + 2 and y is greater than x – 1. The area to the left or right of each line is shaded different colors with the overlapping area also shaded a different color. Both lines are dotted.
285.
This figure shows a graph on an x y-coordinate plane of y is less than 2x - 1 and y is less than or equal to -(1/2)x + 4. The area to the left or below each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
287.
This figure shows a graph on an x y-coordinate plane of x – y is greater than 1 and y is less than –(1/4)x + 3. The area to the right or below each line is shaded different colors with the overlapping area also shaded a different color. Both lines are dotted.
289.
This figure shows a graph on an x y-coordinate plane of 3x – y is less than or equal to 6 and y is greater than or equal to –(1/2)x. The area to the right or above each line is shaded different colors with the overlapping area also shaded a different color.
291.
This figure shows a graph on an x y-coordinate plane of 2x – 5y is less than 10 and 3x +4y is greater than or equal to 12. The area to the right above each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
293.
This figure shows a graph on an x y-coordinate plane of 2x + 2y is greater than -4 and –x + 3y is greater than or equal to 9. The area to the right or above each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
295.
This figure shows a graph on an x y-coordinate plane of x – 2y is less than 3 and y is less than or equal to 1. The area to the left or below each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
297.
This figure shows a graph on an x y-coordinate plane of y is greater than or equal to (-1/2)x - 3 and x is less than or equal to 2. The area to the left or right of each line is shaded different colors with the overlapping area also shaded a different color.
299.
This figure shows a graph on an x y-coordinate plane of y is greater than or equal to (3/4)x - 2 and y is less than 2. The area to the left or below each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
301.
This figure shows a graph on an x y-coordinate plane of 3x – 4y is less than 8 and x is less than 1. The area to the left of each line is shaded different colors with the overlapping area also shaded a different color. Both lines are dotted.
303.
This figure shows a graph on an x y-coordinate plane of x is greater than or equal to 3 and y less than or equal to 2. The area to the right or below each line is shaded different colors with the overlapping area also shaded a different color.
305.

No solution

This figure shows a graph on an x y-coordinate plane of 2x + 4y is greater than 4 and y is less than or equal to (-1/2)x - 2. The area to the left or right of each line is shaded different colors. There is no area where the shaded areas overlap. One line is dotted.
307.

No solution

This figure shows a graph on an x y-coordinate plane of -2x + 6y is less than 0 and 6y is greater than 2x + 4. The area to the left or right of each line is shaded different colors. There is no area where the shaded areas overlap. Both lines are dotted.
309.
This figure shows a graph on an x y-coordinate plane of y is greater than or equal to -3x + 2 and 3x + y is greater than 5. The area to the right of each line is shaded different colors. One line is within the shaded area of the other. One line is dotted.
311.

x+4y<6x+4y<6

This figure shows a graph on an x y-coordinate plane of y is less than or equal to (negative 1/4)x – 2 and x + 4y is less than 6. The area below each line is shaded different colors. One line is within the shaded area of the other. One line is dotted.
313.

−2x+6y>8−2x+6y>8

This figure shows a graph on an x y-coordinate plane of 3y is greater than x + 2 and -2x + 6y is greater than 8. The area above each line is shaded different colors. One line is within the shaded area of the other. Both lines are dotted.
315.
  1. {p+l6015p+10l800{p+l6015p+10l800

  2. This figure shows a graph on an x y-coordinate plane of p + l is greater than or equal to 60 and 15p + 10l is greater than or equal to 800. The area to the left of each line is shaded different colors with the overlapping area also shaded a different color.
  3. No
  4. Yes
317.
  1. {7p+3c500p2c+4{7p+3c500p2c+4

  2. This figure shows a graph on an x y-coordinate plane of 7p + 3c is less than or equal to 500 and p is greater than or equal to 2c + 4. The area to the left or below each line is shaded different colors with the overlapping area also shaded a different color.
  3. Yes
  4. No
319.
  1. {90b+150g5000.35b+2.50g15{90b+150g5000.35b+2.50g15

  2. This figure shows a graph on an x y-coordinate plane of 90b + 150g is greater than or equal to 500 and 0.35b + 2.50g is less than or equal to 15. The area to the right or below each line is shaded different colors with the overlapping area also shaded a different color.
  3. No
  4. Yes
321.
  1. {7c+11p35110c+22p200{7c+11p35110c+22p200

  2. This figure shows a graph on an x y-coordinate plane of 7c + 11p is greater than or equal to 35 and 110c + 22p is less than or equal to 200. The area to the left or right of each line is shaded different colors with the overlapping area also shaded a different color.
  3. Yes
  4. No
323.
  1. {3a+3c<752a+4c<62{3a+3c<752a+4c<62

  2. This figure shows a graph on an x y-coordinate plane of 3a + 3c is less than 75 and 2a + 4c is less than 62. The area to the left ofeach line is shaded different colors with the overlapping area also shaded a different color. Both lines are dotted.
  3. No
  4. Yes
325.

Answers will vary.

Review Exercises

327.

no yes

329.

(3,−3)(3,−3)

This figure shows a graph on an x y-coordinate plane of 3x plus y = 6 and x plus 3y = negative 6.
331.

(5,4)(5,4)

This figure shows a graph on an x y-coordinate plane of 2x – y = 6 and y = 4.
333.

coincident lines

This figure shows a graph on an x y-coordinate plane of 2x – y = 5 and 4x – 2y = 10.
335.

infinitely many solutions, consistent system, dependent equations

337.

no solutions, inconsistent system, independent equations

339.

LaVelle needs 8 ounces of chocolate syrup and 40 ounces of coffee.

341.

(−1,2)(−1,2)

343.

(−2,−2)(−2,−2)

345.

no solution

347.

The numbers are 22 and 33.

349.

The measures are 23 degrees and 67 degrees.

351.

(1,11)(1,11)

353.

(4,−1)(4,−1)

355.

(−2,5)(−2,5)

357.

The numbers are −37−37 and −53−53.

359.

elimination

361.

{x+y=−32x=2y2{x+y=−32x=2y2

363.

{j+d=7200d=j+1600{j+d=7200d=j+1600

365.

Pam is 51 and Jan is 48.

367.

The measures are 119 degrees and 61 degrees.

369.

The pergola is 8 feet high and 12 feet wide.

371.

It will take Lenore 3 hours.

373.

The rate of the boat is 10.5 mph. The rate of the current is 1.5 mph.

375.

Lynn bought 227 student tickets and 34 adult tickets.

377.

Yumi should use 4 cups of candies and 8 cups of nuts.

379.

Jack should put $3600 into savings and $8400 into the CD.

381.

yes no

383.
This figure shows a graph on an x y-coordinate plane of y is less than 3x + 1 and y is greater than or equal to -x - 2. The area to the right of each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
385.
This figure shows a graph on an x y-coordinate plane of 2x – 3y is less than 6 and 3x + 4y is greater than or equal to 12. The area to the left or right of each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
387.

No solution

This figure shows a graph on an x y-coordinate plane of x + 3y is less than 5 and y is greater than or equal to -(1/3)x + 6. The area to the above or below each line is shaded different colors. There is no overlapping shaded area. One line is dotted.
389.


{b+n4012b+18n500{b+n4012b+18n500

This figure shows a graph on an x y-coordinate plane of b + n is less than or equal to 40 and 12b + 18n is greater than or equal to 500. The area to the left or right of each line is shaded different colors with the overlapping area also shaded a different color.


yes
no

Practice Test

391.

yes no

393.
This figure shows a graph on an x y-coordinate plane x – y is greater than -2 and y is less than or equal to 3x + 1. The area to the left of each line is shaded different colors with the overlapping area also shaded a different color. One line is dotted.
395.

(4,−7)(4,−7)

397.

infinitely many solutions

399.

The numbers are 40 and 64

401.

The measures of the angles are 28 degrees and 62 degrees.

403.

It will take Kathy 1616 of an hour (or 10 minutes).

405.

Liz bought 23 children’s tickets and 5 adult tickets.

407.


{C+0.5L50L3C{C+0.5L50L3C

This figure shows a graph on an x y-coordinate plane of C + 0.5L is less than or equal to 50 and L is greater than or equal to 3C. The area to the left or right of each line is shaded different colors with the overlapping area also shaded a different color.


No
Yes

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