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Ideas Math Book Algebra 1 Chapter 5 Solving Systems of Linear Equations Answer key Topicwise and download them for free & prepare very well. Here is the complete list of topic-wise Big Ideas Math Book Algebra 1 Chapter 5 Solving Systems of Linear Equations Solution Key which covers the questions from the BIM Textbooks based on the latest Common Core Curriculum. Ch 5 Big Ideas Math Textbook Algebra 1 Answers material given here offers Questions from Exercises(5.1 to
5.7), Chapter Tests, Review Tests, Quiz, Assessment Tests, Cumulative Assessments, etc. Practice thoroughly and gain more subject knowledge on the concepts of BIM Math Book Algebra 1 Chapter 5 Solutions. Graph the equation. Question 2. Question 3. Question 4. Solve the inequality. Graph the solution. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Solving Systems of Linear Equations Mathematical PracticesMathematically proficient students use technological tools to explore concepts. Monitoring Progress Use a graphing calculator to find the point of intersection of the graphs of the two linear equations. Question 2. Question 3. Lesson 5.1 Solving Systems of Linear Equations by GraphingEssential Question How can you solve a system of linear equations? EXPLORATION 1 Writing a System of Linear EquationsWork with a partner. Your family opens a bed-and-breakfast. They spend $600 preparing a bedroom to rent. The cost to your family for food and utilities is $15 per night. They charge $75 per night to rent the bedroom. b. Write an equation that represents the revenue (income). c. A set of two (or more) linear equations is called a system of linear equations. Write the system of linear equations for this problem. Answer: a. C = 15 . x + $600 C = 15x + 600 b. R = $75 . x R = 75x c. C = 15x + 600 y = 15x + 600 R = 75x y = 75x EXPLORATION 2 Using a Table or Graph to Solve a System b. How many nights does your family need to rent the bedroom before breaking even? c. In the same coordinate plane, graph the cost equation and the revenue equation from Exploration 1. d. Find the point of intersection of the two graphs. What does this point represent? How does this compare to the break-even point in part (b)? Explain. Answer: R = 75x b. 11 nights Communicate Your Answer Question 3. Question 4. b. y = x c. y = -x – 1 Monitoring Progress Tell whether the ordered pair is a solution of the system of linear equations. Question 2. Solve the system of linear equations by graphing. Question 4. Question 5. Question 6. Solving Systems of Linear Equations by Graphing 5.1 ExercisesVocabulary and Core Concept Check Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3–8, tell whether the ordered pair is a solution of the system of linear equations. Question 4. Question 5. Question 6. Question 7. Question 8. In Exercises 9–12, use the graph to solve the system of linear equations. Check your
solution. Answer: Question 10. Answer: Question 11. Answer: Question 12. Answer: In Exercises 13–20, solve the system of linear equations by graphing. Question 14. y = 0 Question 15. Question 16. Question 17. Question 18. Question 19. Question 20. ERROR ANALYSIS In Exercises 21 and 22, describe and correct the error in solving the system of linear equations. Answer: Question 22. Answer: USING TOOLS In Exercises 23–26, use a graphing calculator to solve the system of linear equations. Question 24. Question 25. Question 26. Question 27. Answer: Question 28. Answer: Question 29. Answer: Question 30. Question 31. Question 32. a. For what numbers of binders are the costs the same at two different companies? Explain. b. How do your answers in part (a) relate to systems of linear equations? Answer: Question 33. a. Write and graph a system of linear equations that represents this situation. b. Your friend says that after an hour of hiking you will both be at the same location on the trail. Is your friend correct? Use the graph from part (a) to explain your answer. Answer: Maintaining Mathematical Proficiency Solve the literal equation for y. Question 35. Question 36. Lesson 5.2 Solving Systems of Linear Equations by SubstitutionEssential Question How can you use substitution to solve a system of linear equations? EXPLORATION 1 Using Substitution to Solve Systems Method 2 Solve for y first. b. x – 6y = -11 x – 6y = -11 c. 4x + y = -1 20x + 5y = -5 EXPLORATION 2 Writing and Solving a System of Equations Communicate Your Answer Question 3. Question 4. 2x + 4y = -14 b.x – 2y = -6 x – 2y = -6 c.-3x + 2y = -10 -3x + 2y = -10 d. 3x + 2y = 13 3x + 2y = 13 e. 3x – 2y = 9 3x – 2y = 9 f. 3x – y = -6 15x – 5y = -30 Monitoring Progress Solve
the system of linear equations by substitution. Check your solution. Question 2. Question 3. Solve the system of linear equations by substitution.
Check your solution. Question 5. Question 6. Question 7. Question 8. Solving Systems of Linear Equations by Substitution 5.2 ExercisesVocabulary and Core Concept Check Question 2. Monitoring Progress and Modeling with Mathematics In Exercises 3−8, tell which equation you would choose to solve for one of the variables. Explain. Question 4. Question 5. Question 6. Question 7. Question 8. In Exercises 9–16, solve the system of linear equations by substitution. Check your solution. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Answer: Question 18. Answer: Question 19. Question 20. Answer: In Exercises 21–24, write a system of linear equations that has the ordered pair as its solution. Question 22. Question 23. Question 24. Question 25. Question 26. Answer: MATHEMATICAL CONNECTIONS In Exercises 27 and 28, (a) write an equation that represents the sum of the angle measures of the triangle and (b) use your equation and the equation shown to find the values of x and y. Answer: Question 28. Answer: Question 29. Question 30. Question 31. Question 32. a. At what point do the lines appear to intersect? b. Could you solve a system of linear equations by substitution to check your answer in part (a)? Explain. Answer: Question 33. Question 34. Question 35. Maintaining Mathematical Proficiency Find the
sum or difference. Question 37. Question 38. Question 39. Question 40. Question 41. Lesson 5.3 Solving Systems of Linear Equations by EliminationEssential Question How can you use elimination to solve a system of linear equations? EXPLORATION 1 Writing and Solving a System of Equations Label one of the equations Equation 1 and the other equation Equation 2. b. Subtract Equation 1 from Equation 2. Explain how you can use the result to solve the system of equations. Then find and interpret the solution. EXPLORATION 2 Using Elimination to Solve Systems Method 2 Add. Add the two equations. Then use the result to solve the system. Is the solution the same using both methods? Which method do you prefer? a. 3x – y = 6 3x + y = 0 b. 2x + y =
6 c. x – 2y = -7 EXPLORATION 3 Using Elimination to Solve a System Communicate Your Answer Question 4. Question 5. Question 6. Monitoring Progress Solve the system of linear equations by elimination. Check your solution. Question 2. Question 3. Question 4. Solving Systems of Linear Equations by Elimination 5.3 ExercisesVocabulary and Core Concept Check Question 2. Monitoring Progress and Modeling with Mathematics In Exercises 3−10, solve the system of linear equations by elimination. Check your solution. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. In Exercises 11–18, solve the system of linear equations by elimination. Check your solution. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Question 18. Question 19. Answer: Question
20. Answer: Question 21. Answer: Question 22. Answer: In Exercises 23–26, solve the system of linear equations using any method. Explain why you chose the method. Question 24. Question 25. Question 26. Question 27. Question 28. a. Estimate the numbers of students who chose breakfast and lunch. b. The number of students who chose lunch was 5 more than the number of students who chose breakfast. Write a system of linear equations that represents the numbers of students who chose breakfast and lunch. c. Explain how you can solve the linear system in part (b) to check your answers in part (a). Answer: Question 29. Question 30. Question 31. a. Write and solve a system of linear equations to find the length and width of the original rectangle. b. Find the length and width of the new rectangle. Answer: Question 32. Answer: Question 33. Question 34. Question 35. Maintaining Mathematical Proficiency Solve the equation. Determine whether the equation has one solution, no solution, or infinitely many solutions. Question 37. Question 38. Question 39. Write an equation of the line that passes through the given point and is parallel to the given line. Question 41. Question 42. Lesson 5.4 Solving Special Systems of Linear EquationsEssential Question Can a system of linear equations have no solution or infinitely many solutions? EXPLORATION 1 Using a Table to Solve a System b. When will your company break even? What is wrong? EXPLORATION 2 Writing and Analyzing a System c. Can you find the weight of each type of bead? Explain your reasoning. Communicate Your Answer Question 3. Question 4. Answer: Monitoring Progress Solve the system of linear
equations. Question 2. Question 3. Question 4. Question 5. Solving Special Systems of Linear Equations 5.4 ExercisesVocabulary and Core Concept Check Question 2. Monitoring Progress and Modeling with Mathematics In Exercises 3−8, match the system of linear equations with its graph. Then determine whether the system has one solution, no solution, or infinitely
many solutions. Question 4. Question 5. Question 6. Question 7. Question 8. In Exercises 9–16, solve the system
of linear equations. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. In Exercises 17–22, use only the slopes and y-intercepts of the graphs of the equations to determine whether the system of linear equations has one solution, no solution, or infinitely many solutions. Explain. Question 18. Question 19. Question 20. Question 21. Question 22. ERROR ANALYSIS In Exercises 23 and 24, describe and correct the error in solving the system of linear equations. Answer: Question 24. Answer: Question 25. Answer: Question 26. Question 27. Answer: Question 28. Question 29. Question 30. a. Estimate the distance at which Team C’s runner passed Team B’s runner. b. If the race was longer, could Team C’s runner have passed Team A’s runner? Explain. c. If the race was longer, could Team B’s runner have passed Team A’s runner? Explain. Answer: Question 31. Question 32. Answer: Maintaining Mathematical Proficiency Solve the equation. Check your solutions. Question 34. Question 35. Question 36. Solving Systems of Linear Equations Study Skills: Analyzing Your Errors5.1 – 5.4 What Did You Learn? Core
Vocabulary Core Concepts Section 5.2 Section 5.3 Section 5.4 Mathematical Practices Question 1. Question 2. Question 3. Study Skills: Analyzing Your Errors Study Errors Solving Systems of Linear Equations 5.1–5.4 QuizUse the graph to solve the system of linear equations. Check your solution. Answer: Question 2. Answer: Question 3. Answer: Solve the system of linear equations by substitution. Check your solution. Question 5. Question 6. Solve the system of linear equations by elimination. Check your solution. Question 8. Question 9. Solve the system of linear equations. Question 11. Question 12. Question 13. a. Write a system of linear equations that represents this situation. b. Solve the system by graphing. Interpret your solution. Answer: Question 14. Question 15. Answer: Lesson 5.5 Solving Equations by GraphingEssential Question How can you use a system of linear equations to solve an equation with variables on both sides? Previously, you learned how to use algebra to solve equations with variables on both sides. Another way is to use a system of linear equations. EXPLORATION 1 Solving an Equation by Graphing c. Explain why this “graphical method” works. EXPLORATION 2 Solving Equations Algebraically and Graphically Communicate Your Answer Question 3. Question 4. Monitoring Progress Solve the equation by graphing. Check your solution. Question 2. Solve the equation by graphing. Check your solutions. Question 4. Question 5. Solving Equations by Graphing 5.5 ExercisesVocabulary and Core Concept Check Question 2. Monitoring Progress and Modeling with Mathematics In Exercises 3–6, use the graph to solve the equation. Check your solution. Answer: Question
4. Answer: Question 5. Answer: Question
6. Answer: In Exercises 7−14, solve the equation by graphing. Check your solution. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. In Exercises 15−20, solve the equation by graphing. Determine whether the equation has one solution, no solution, or infinitely many solutions. Question 16. Question 17. Question 18. Question 19. Question 20. In Exercises 21 and 22, use the graphs to solve the equation. Check your solutions. Answer: Question 22. Answer: In Exercises 23−30, solve the equation by graphing. Check your solutions. Question 24. Question 25. Question 26. Question 27. Question 28. Question 29. Question 30. USING
TOOLS In Exercises 31 and 32, use a graphing calculator to solve the equation. Question 32. Question 33. Question 34. Answer: Question 35. Question 36. Question 37. Question 38. a. Estimate the point of intersection of the graphs. b. Interpret your answer in part (a). Answer: Question 39. Answer: Question 40. Question 41. Question 42. Question 43. Question 44. Question 45. Use the graphs of f and g to describe the transformation from the graph of f to the graph of g. Question 47. Question 48. Question 49. Lesson 5.6 Graphing Linear Inequalities in Two VariablesEssential Question How can you graph a linear inequality in two variables? EXPLORATION 1 Writing a Linear Inequality in Two Variables c. Write an inequality represented by the graph. Which inequality symbol did you use? Explain your reasoning. EXPLORATION 2 Using a Graphing Calculator Work with a partner. Use a graphing calculator to graph y ≥ \(\frac{1}{4}\)x – 3. a. Enter the equation y = \(\frac{1}{4}\)x – 3 into your calculator. b. The inequality has the symbol ≥. So, the region to be shaded is above the graph of y = \(\frac{1}{4}\)x – 3, as shown. Verify this by testing a point in this region, such as (0, 0), to make sure it is a solution of the inequality. Because the inequality symbol is greater than or equal to, the line is solid and not dashed. Some graphing calculators always use a solid line when graphing inequalities. In this case, you have to determine whether the line should be solid or dashed, based on the inequality symbol used in the original inequality EXPLORATION 3 Graphing Linear Inequalities in Two Variables Communicate Your Answer Question 4. Question 5. Monitoring Progress Tell whether the ordered pair is a solution of the inequality. Question 2. Question 3. Question
4. Graph the inequality in a coordinate plane. Question 6. Question 7. Question 8. Question 9. Graphing Linear Inequalities in Two Variables 5.6 ExercisesVocabulary and Core Concept Check Question 2. Monitoring Progress and Modeling with Mathematics In Exercises 3–10, tell whether the ordered pair is a solution of the inequality. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. In Exercises 11−16, tell whether the ordered pair is a solution of the inequality whose graph is shown. Question 11. (0, -1) Answer: Question 12. Question 13. Question 14. Question 15. Question
16. Question 17. Answer: Question
18. In Exercises 19–24, graph the inequality in a coordinate plane. Question 20. Question 21. Question 22. Question 23. Question
24. In Exercises 25−30, graph the inequality in a coordinate plane. Question 26. Question 27. Question 28. Question 29. Question 30. ERROR ANALYSIS In Exercises 31 and 32, describe and correct the error in graphing the inequality. Answer: Question
32. Answer: Question 33. Question 34. Answer: In Exercises 35–38, write an inequality that represents the graph. Answer: Question
36. Answer: Question 37. Answer: Question 38. Answer: Question 39. a. Write and graph an inequality that represents the numbers of large and small boxes a 200-pound delivery person can take on the elevator. b. Explain why some solutions of the inequality might not be practical in real life. Answer: Question 40. Answer: Question 41. Question 42. Question 43. CRITICAL THINKING Question 45. Maintaining Mathematical Proficiency Write the next three terms of the arithmetic sequence. Question 47. Question 48. Lesson 5.7 Systems of Linear InequalitiesEssential Question How can you graph a system of linear inequalities? EXPLORATION 1 Graphing Linear Inequalities EXPLORATION 2 Graphing a System of Linear Inequalities b. Describe each of the shaded regions of the graph. What does the unshaded region represent? Communicate Your Answer Question 3. How can you graph a system of linear inequalities? Answer: Question 4. Question 5. Question 6. Monitoring Progress Tell whether the ordered pair is a solution of the system of linear inequalities. Question 2. Graph the system of linear inequalities. Question 4. Question 5. Write a system of linear inequalities represented by the graph. Answer: Question 7. Answer: Question 8. Question 9. Systems of Linear Inequalities 5.7 ExercisesVocabulary
and Core Concept Check Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3−6, tell whether the ordered pair is a solution of the system of linear inequalities. Question 3. (-4, 3) Answer: Question 4. Question 5. Question 6. In Exercises 7−10, tell whether the ordered pair is a solution of the system of linear inequalities. Question 8. Question 9. Question 10. In Exercises 11−20, graph the system of linear inequalities. Question 12. Question 13. Question 14. Question 15. Question 17. Question 18. Question 19. Question 20. In Exercises 21−26, write a system of linear inequalities represented by the graph. Answer: Question
22. Answer: Question 23. Answer: Question
24. Answer: Question 25. Answer: Question
26. Answer: ERROR ANALYSIS In Exercises 27 and 28, describe and correct the error in graphing the system of linear inequalities. Answer: Question
28. Answer: Question 29. a. Write and graph a system of linear inequalities that represents the situation. b. Identify and interpret a solution of the system. c. Use the graph to determine whether you can buy 4 pounds of blueberries and 1 pound of strawberries. Answer: Question 30. Question 31. Answer: Question 32. Question 33. Question 34. Question 35. Question 36. Question 37. Question 38. Replace the equal signs with inequality symbols to create a system of linear inequalities that has point C as a solution, but not points A, B, and D. Explain your reasoning. Answer: Question 39. Question 40. Question 41. OPEN-ENDED In Exercises 42−44, write a system of linear inequalities with the given characteristic. Question 43. Question 44. Question 45. Question 46. Question 47. Question 48. a. Write and graph a system of four linear inequalities that represents the number x of necklaces and the number y of key chains that you can make. b. Find the vertices (corner points) of the graph of the system. c. You sell each necklace for $10 and each key chain for $8. The revenue R is given by the equation R = 10x + 8y. Find the revenue corresponding to each ordered pair in part (b). Which vertex results in the maximum revenue? Answer: Maintaining Mathematical Proficiency Write the product using exponents. Question
50. Question 51. Write an equation of the line with the given slope and
y-intercept. Question 53. Question 54. Question 55. Solving Systems of Linear Equations Performance Task: Prize Patrol5.5–5.7 What Did You Learn? Core Vocabulary Core Concepts Section 5.6 Section 5.7 Mathematical Practices Question 1. Question 2. Question 3. Performance Task Prize Patrol You have been selected to drive a prize patrol cart and place prizes on the competing teams’ predetermined paths. You know the teams’ routes and you can only make one pass. Where will you place the prizes so that each team will have a chance to find a prize on their route? Solving Systems of Linear Equations Chapter Review5.1 Solving Systems of Linear Equations by Graphing (pp. 235–240) Solve the system of linear equations by graphing. Question 2. Question 3. 5.2 Solving Systems of Linear Equations by Substitution (pp. 241–246) Solve the system of linear equations by substitution. Check your solution. Question 5. Question 6. Question 7. 5.3 Solving Systems of Linear Equations by Elimination (pp. 247 – 252) Solve the system of linear equations by elimination. Check your solution. Question 9. Question 10. 5.4 Solving Special Systems of Linear Equations (pp. 253–258) Solve the system of linear equations. Question 12. Question 13. 5.5 Solving Equations by Graphing (pp. 261–26 Solve the equation by graphing. Check your solution(s). Question 15. Question 16. 5.6 Graphing Linear Inequalities in Two Variables (pp. 267–272) Graph the inequality in a coordinate plane. Question 18. Question 19. Question 22. Solving Systems of Linear Equations Chapter TestSolve the system of linear equations using any method. Explain why you chose the method. Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Graph the system of linear inequalities. Question 10. Question 11. Question 12. a. Is there enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain. b. The receipt shown is for buying the same gasoline and same oil. Is there now enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain. c. Determine the cost of 1 gallon of gasoline and 1 quart of oil. Answer: Question 13. Question
14. a. Write and graph an inequality that represents the numbers of trophies and medals you can buy. Identify and interpret a solution of the inequality. b. You want to purchase at least 6 items. Write and graph a system that represents the situation. How many of each item can you buy? Answer: Question 15. Solving Systems of Linear Equations Cumulative AssessmentQuestion 1. Answer: Question 2. Answer: Question
3. Answer: Question 4. Answer: Question 5. Answer: Question
6. Answer: Question 7. Answer: Question 8. Answer: Question
9. Answer: Question 10. Answer: |