Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 1
7.1 Graphs of Linear Systems
Answers
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 2
8.
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Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 3
11.
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Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 4
14.
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16.
a. Looks like it should be at (−2, 4) b. No, (−2, 4) does not work.
c. The values are not integers
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 5
17.
b. No, they do not have the same slope
c. Extend the graph to include = 36
18.
b. Set bounds to 5 ≤ ≤ 10 5 ≤ ≤ 10
19. 6.6 years
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 6
7.2 Systems Using Substitution
12. The angles are 99° and 81°
13. Jason is 14, Becky is 9
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 7
7.3 Mixture Problems
b. No, minimum price for 5lbs is $11
c. 6.81lb (all peanuts)
a. 0.8L of 10% solution and 0.2L of 35% solution
b. 1.6L of 10% solution and 0.4L of 35% solution
3. The bracelet density is 16.37 g/cc
4. 82 purchased in advance and 38 at the door
5. 10 gal of 40% and 5 gal of 100%
6. 25 multiple choice and 10 short answer
7. 23 multiple choice and 8 short answer
8. 4 multiple choice and 1 short answer
9. 1st way: + = 5, 2 + 5 = 13 2nd way: + = 30, 2 + 5 = 87
10. Calculate what Kwan missed rather than what she got right: + = 4, 2 + 5 = 14
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 8
7.4 Linear Systems with Addition or Subtraction
Answers
5. Candy bars cost $0.48 and fruit roll-ups cost $0.35
6. The wind speed is 24 miles per hour.
7.
b. The rate per mile is $1.12
c. A seven-mile trip is $8.69
8. $0.75 per minute for the first five minutes, and $0.25 per minute thereafter.
9. The plumber worked 6.25 hours and the builder worked 4 hours.
10. Paul makes $6.20 per hour with a $12 bonus per warranty.
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 9
7.5 Linear Systems with Multiplication
Answers
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 10
7.6 Comparing Methods for Solving Linear Systems
Answers
7. Angle A = 114° and angle B = 66°
8. There should be 148.8 L of the 5% solution and 48.8 L of the 15% solution.
9. The pieces are 99 yards and 51 yards in length.
10. Mr. Stein invested $68,750 in company A, and $31,250 in company B.
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 11
7.7 Consistent and Inconsistent Linear Systems
Answers
2. = − 3
3. = 3
4. = − 1 : System is dependent.
5. = 1
1
6. = 2 + 1 and = − 3
2 − 6 :System is consistent
7. = −3 + 4 and = −3 + 5 : System is independent
8. = 1
9. = 2 − 4 : System is dependent
10. = 2 − 3 and = −3 + 6 : System is consistent
11. = − 1
5 + 24 and = − + 24 : System is consistent
12. = − 3
3
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 12
7.8 Determining the Type of Linear System
Answers
4. System is independent
6. System is dependent
9. System is independent
11. ( 3
12. (1 7
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 13
7.9 Applications of Linear Systems
Answers
2. The cost is the same after 5 1
3 months
3. Ties are $23, and suspenders are $47
4. The plane flies at 540mph in still air, and the jet stream is 60mph.
5. 350 children and 850 adults
6. Not possible, the maximum take is $9,600
7. 300 16-oz sodas, and 240 32-oz sodas
8. Peter discovered that Nadia would have had to pay a different price for each apple or
banana (or both) each time for the second purchase to have been $6.
9. Apples cost less than $1.25 each, and bananas cost less than $2.50 each.
10. Four apples cost $3.00. Apples cost $0.75 each and bananas $1.00 each.
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 14
7.10 Systems of Linear Inequalities
Answers
1. The system is inconsistent because neither inequality includes the line = 3 − 5.
2. The system is consistent because both inequalities include = 2 + 3.
3. The system is inconsistent because only one inequality includes the line = − + 1.
4.
a. Changing the inequality makes the system inconsistent.
b. Answers will vary, but should include an inequality that completely encloses the original
solution.
c. Answers will vary but should include an inequality that does not include any area in the
solution to the original system.
5.
a. Answers will vary for the additional inequality, but it should not include any area in > 3.
b. ≤ 4 and = 0
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 15
6.
7.
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Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 16
9.
10.
11.
Chapter 7 – Solving Systems of Equations and Inequalities Answer Key
CK-12 Algebra I Concepts 17
7.11 Linear Programming
(0, 0) (4, −4) (3, −1)
The maximum value of is 0 and the minimum value of is -20
2. 4 apprentices and 5 senior
3. 368 trucks
5. 320 trucks, zero left over canes
6. 8.4 bookcases and 9.6 t.v. stands – does not makes sense (not whole values)
7. = 8 or = 9, and = 9 or = 10
8. 8, 9 and 9, 9
9. 9, 9 = $1,440
10. 10, 8 = $1,400
11. 7, 10 = $1,420