Skills Practice Skills Practice for Lesson 2.1

Transcription

1 Skills Practice Skills Practice for Lesson.1 Name Date Finding a Job Introduction to Systems of Linear Equations Vocabulary Write the term that best completes each statement. 1. A(n) is the location on a graph where two or more lines meet indicating that the values are the same.. A(n) is two or more linear equations in the same variables. Problem Set Complete each table. Then determine the point where the two lines intersect Carnegie Learning, Inc. x y x y 3x x y x 3 y x x y x y x 6 x y x 4 y x Chapter Skills Practice 45

2 7. 8. x 10 5 y x y x 7 x y 1 x y x x y x y x 6 x y x 4 y 4x Graph both equations on the same coordinate grid. Determine the point where the two lines intersect. 11. y 3x and y 5x 1. y x and y 4x 009 Carnegie Learning, Inc. 46 Chapter Skills Practice

3 Name Date 13. y x 1 and y x y x 5 and y x y 4x and y 6x y x 5 and y x Carnegie Learning, Inc. For each situation, explain what the point of intersection of the two equations represents. 17. The cost in dollars of making x DVDs is given by the equation y x The revenue r in dollars of selling x DVDs is given by y 1x. Chapter Skills Practice 47

4 18. A police car needs to catch a speeding car. The speeding car is already 10 miles ahead of the police car. The distance the speeding car travels is given by the equation y 100x 10, where x represents the time in hours. The distance the police car travels is given by the equation y 110x, where x represents the time in hours. 19. The amount of water a plant needs in liters after t months is given by the equation y 0.1t. The amount of water that a planter can hold in liters after t months is given by the equation y The capacity of a garage after t months is given by the equation y 750. The number of cars in the garage after t months is given by the equation y 15t The amount of hard drive space in gigabytes that a computer uses t months after it was bought is given by the equation y 0t 30. The amount of space left on the hard drive in gigabytes t months after it was bought is given by the equation y 0t 0.. The cost to buy one gigabyte of hard drive space in dollars after t months is given by the equation y 0.5t 4. The cost to make one gigabyte of hard drive space in dollars after t months is given by the equation y 0.10t Carnegie Learning, Inc. 48 Chapter Skills Practice

5 Skills Practice Skills Practice for Lesson. Name Date Pens-R-Us Solving Systems of Linear Equations: Graphing and Substitution Vocabulary Give an example of how to solve a system of two equations by using the given method. 1. substitution. graphing Problem Set 009 Carnegie Learning, Inc. Use the slope and y-intercept to graph the equations. Then determine the point of intersection. y x 3 3. y x 1 4. y x 5 y x 4 Chapter Skills Practice 49

6 y x 5. y 3x 4 y 4x 4 6. y x 9 7. y 1 x 5 y x 7 8. y 1 5 x 4 y x 009 Carnegie Learning, Inc. 50 Chapter Skills Practice

7 Name Date 9. y 3 x 6 y x 10. y 3 x 3 y 3x 8 y 6x y 3x y 1.5x 8 y 3x Carnegie Learning, Inc. Chapter Skills Practice 51

8 Use algebraic substitution to solve each system of equations. x y 13. x y 4 x y x y x y x y 4 x y x y 5 x y y x 18. x y 8 y x Carnegie Learning, Inc. 5 Chapter Skills Practice

9 Name Date y 3x x y 3 y x 7 0. x y 8 y 1.5x y x 10. y.3x 565 y 3.8x Carnegie Learning, Inc. Chapter Skills Practice 53

10 009 Carnegie Learning, Inc. 54 Chapter Skills Practice

11 Skills Practice Skills Practice for Lesson.3 Name Date Tickets Solving Systems of Linear Equations: Linear Combinations Vocabulary For the two equations x 3y 7 and 4x y, explain how you would use linear combinations to eliminate each variable. 1. Eliminate the x variable.. Eliminate the y variable. 009 Carnegie Learning, Inc. Problem Set Use the slope and y-intercept to graph the equations. Then determine the point of intersection. y x 5 y 4. y 1 x 1 3 x 3 y 1 4 x Chapter Skills Practice 55

12 y x 1 y 1 3 x 6. y 1 3 x 4 y 3 x 4 Use algebraic substitution to solve each system of equations. x y 9 7. x y 1 8. x 3y 7 x 4y Carnegie Learning, Inc. 56 Chapter Skills Practice

13 Name Date 3x y 3 9. x 4y 10 4x y x 3y 8 Use linear combinations to solve each system of equations. x y x y 1. x y 6 x y Carnegie Learning, Inc. Chapter Skills Practice 57

14 x y x y 5 3x y x y 4 3x 4y x 3y x 3y 14 5x 4y Carnegie Learning, Inc. 58 Chapter Skills Practice

15 Name Date 45x 10y x 6y 0 30x 50y x y x 1 y x 1 x y y x 1 y Carnegie Learning, Inc. Chapter Skills Practice 59

16 009 Carnegie Learning, Inc. 60 Chapter Skills Practice

17 Skills Practice Skills Practice for Lesson.4 Name Date Cramer s Rule Solving Systems of Linear Equations: Cramer s Rule Vocabulary Write the term that best completes each statement. 1. Graphing, substitution, linear combinations, and Cramer s Rule are all methods for solving.. An algebraic operation that transforms an n n array of numbers into a single value is called calculating the. 3. uses determinants to solve a system of linear equations in two variables. 4. A(n) array is made up of n n numbers. 009 Carnegie Learning, Inc. Problem Set Calculate the value of each determinant Chapter Skills Practice 61

18 User Cramer s Rule to solve each system of equations. 15. x 3y x y 16. 3x 4y 1 x y x 0.y 4 x y Carnegie Learning, Inc. 6 Chapter Skills Practice

19 Name Date x 3y 1 0.3x y y 7 x 1 y x y 10 4 x Carnegie Learning, Inc. 1. y 5x 1 y 5x 3 Chapter Skills Practice 63

20 . y 4x 1 y 8x 4 3. x 3y 4 x 9y 3 4. x 8y 4 3x 16y Carnegie Learning, Inc. 64 Chapter Skills Practice

21 Skills Practice Skills Practice for Lesson.5 Name Date Consistent and Independent Solving Systems of Linear Equations: Consistent and Independent Vocabulary Define each term in your own words. 1. consistent system of equations. inconsistent system of equations 3. linearly independent system of equations 4. linearly dependent system of equations 009 Carnegie Learning, Inc. Problem Set Choose any method to solve each system of equations. y x 4 5. y x 5 y x 5 6. y x x y 7. x y 6 8. x y 7 x y 5 Chapter Skills Practice 65

22 3x y 1 9. x y 4 x 4y x 4y 4 x 3y y x 9 x y x y 17 x 1 3 y x 4 5 y x 4 y 1 5 Solve each system of equations. Then describe the system s consistency and dependency. x y x y x y x y x y x 4y 18. 3x y 6x y Carnegie Learning, Inc. 66 Chapter Skills Practice

23 Name Date 3x 4y x 8y 6 4x 6y 0. x 9y 61 y x x y y 3x. 6x y 4 y x 3. x y Carnegie Learning, Inc. 4. y x 1x 3y 15 Chapter Skills Practice 67

24 009 Carnegie Learning, Inc. 68 Chapter Skills Practice

25 Skills Practice Skills Practice for Lesson.6 Name Date Inequalities Infinite Solutions Solving Linear Inequalities and Systems of Linear Inequalities in Two Variables Vocabulary Give an example of each term. 1. linear inequality in two variables. equation of a half-plane 3. system of two linear inequalities in two variables 4. inequality 009 Carnegie Learning, Inc. Problem Set Graph each inequality. 5. y x 4 6. y x Chapter Skills Practice 69

26 7. y x 3 8. y 3x 1 9. y 1 x y 3 x 009 Carnegie Learning, Inc. 70 Chapter Skills Practice

27 Name Date Graph the solution to each system of linear inequalities. y x y x 3 y 3x 1. y 5x y 3x 13. y x 14. y x 1 y 4x Carnegie Learning, Inc. Chapter Skills Practice 71

28 y x y 3x 15 y x y 3x 1 y x 8 y 18. y 3 x x 5 y 1 8 x Carnegie Learning, Inc. 7 Chapter Skills Practice

29 Name Date y x 1 y 1 0. y x x 6 y 1 9 x Carnegie Learning, Inc. Chapter Skills Practice 73

30 009 Carnegie Learning, Inc. 74 Chapter Skills Practice

31 Skills Practice Skills Practice for Lesson.7 Name Date Three in Three or More Solving Systems of Three or More Linear Equations in Three or More Variables Vocabulary Explain how the two terms are related determinant and a 3 3 square array Problem Set Evaluate each 3 3 determinant Carnegie Learning, Inc Chapter Skills Practice 75

32 Write a system of three linear equations in three variables to model each situation. Define each variable. 1. The sum of the ages of Marise, Sophia, and Jaren is 45 years. Jaren is six years older than Marise. Sophia is three years older than Marise. 009 Carnegie Learning, Inc. 76 Chapter Skills Practice

33 Name Date 13. The sum of three basketball players' heights, Amna, Wen, and Nireta, is 186 inches. Nireta is inches taller than Wen. Nireta is 7 inches taller than Amna. 14. An office supply store sells flash drives for $0 each, headphones for $15 each, and reams of paper for $5 each. Roger spent a total of $130 on flash drives, headphones, and reams of paper. It cost him $115 for the flash drives and reams of paper. It cost him $90 for the headphones and reams of paper. 009 Carnegie Learning, Inc. 15. At the movies a bag of popcorn costs $3, a box of chocolate-covered raisins costs $.50, and a bottle of water costs $. Erika spent $14 on popcorn, raisins, and bottles of water for her and her friends. The popcorn and raisins totaled $8. The raisins and bottles of water totaled $11. Chapter Skills Practice 77

34 Use substitution to solve each system of equations. 16. x y z 3x y z x 3y z Carnegie Learning, Inc. 78 Chapter Skills Practice

35 Name Date 17. x y z 4 x y z 1 x y z Carnegie Learning, Inc. Chapter Skills Practice 79

36 18. x y z 8 x y z 1 x 3y z Carnegie Learning, Inc. 80 Chapter Skills Practice

37 Name Date 19. x y z 3 x 3y z 4 x y z Carnegie Learning, Inc. Chapter Skills Practice 81

38 Use linear combinations to solve each system of equations. 0. y z 1 x 3y 5z 1 x y 3z 009 Carnegie Learning, Inc. 8 Chapter Skills Practice

39 Name Date 1. 3x y 9 x y 3z 8 5x 4y 3z Carnegie Learning, Inc. Chapter Skills Practice 83

40 . 3 x y z 3 x 3y z 17 1 x y z Carnegie Learning, Inc. 84 Chapter Skills Practice

41 Name Date 3. 3 x 4 y 1 z x 5y 4z 1 x y z Carnegie Learning, Inc. Chapter Skills Practice 85

42 Use Cramer s Rule to solve each system of equations x 3.y 1.8z 1.3 x 5y z 8 y z x.7y 0.5z 0.5 x 3y z 8 x y Carnegie Learning, Inc. 86 Chapter Skills Practice

43 Name Date 6. x 3y 5z 0 x 10y 5z 3 3x y z 9 7. x 4y z 1 x 3y z 4 x y 3z Carnegie Learning, Inc. Chapter Skills Practice 87

44 009 Carnegie Learning, Inc. 88 Chapter Skills Practice