Name: ______________________Class: _________________ Date: _________ ID: A Algebra II Chapter 3 Test Solve the system by graphing. State whether the stystem is independent, dependent, or inconsistent. 1. −3x − 2y = −7 3x − y = 10 Without graphing, is the system independent, dependent, or inconsistent? 2. 12x + 3y = 12 y = −4x + 5 Solve the system by substitution. 3. −2x − y = −14 3x − y = 11 Solve the system using elimination. 4. −4x + 4y = −8 x − 4y = −7 Use Substitution or Elimination. What are the solutions of the following systems? 5. −x + 2y = 10 −3x + 6y = 11 1 Name: ______________________ Solve the system of inequalities by graphing. 6. y ≤ −3x − 1 y > 3x − 2 ID: A Solve the system of inequalities by graphing. 7. y ≥ 4 y > |x − 1 | 2 Name: ______________________ ID: A Graph the system of constraints and find the value of x and y that maximize the objective function. 8. Constraints x ≥ 0 y ≥ 0 y ≤ 1 3 x+2 6 ≥ y+x Objective function: C = 7x − 3y What is the solution of the system? Solve by hand using a matrix. You may use your calculator to double check your answer. You must show all of your work to receive full credit. 9. 2x + 6y = 38 5x − y = 15 3 Name: ______________________ ID: A Solve the system by elimination. You must show all your work to get full credit. (Use the matrix function on your calculator to check your solution) 10. x + 3y + z = −6 2x + y + 3z = −4 −3x − 3y − 3z = 6 Solve the system by substitution. You must show all your work to get full credit. (Use the matrix function on your calculator to check your solution) 11. 2x − y + z = −4 z = 5 −2x + 3y − z = −10 12. What is element a 23 in matrix A? È3 Í Í A= Í 8 Í Í 0 Î 7 4 −4 ˘ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ −6 ˙ ˙ ˙ ˙ ˙ ˙ 6 ˙ ˙ ˙ ˙ ˙ ˙ ˚ 0 4 Name: ______________________ How can you represent the system of equations with a matrix? 13. −4x − 5y = 6 2x − 4y = 2 What linear system of equations does the matrix represent? È Í 14. Í −2 Í Î 14 | ˘ ˙ ˙ | ˙ ˙ −9 | 11 ˙ ˙ ˙ ˙ | ˙ ˙ ˙ −2 || 15 ˙ ˙ ˙ ˙ ˚ ID: A What is the solution of the system of equations? (Use a any method from the chapter so solve. Show your work) 15. −5x + y − 5z = 1 2x + 2y − 3z = −13 3x − y − 5z = −25 16. A food store makes a 11-lb mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 5 ID: A Algebra II Chapter 3 Test Answer Section 1. ANS: (3, –1) PTS: 1 DIF: L2 REF: 3-1 Solving Systems Using Tables and Graphs OBJ: 3-1.1 To solve a linear system using a graph or a table NAT: CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d TOP: 3-1 Problem 1 Using a Graph or Table to Solve a System KEY: system of linear equations | graphing | solution of a system 2. ANS: inconsistent PTS: OBJ: NAT: TOP: KEY: 3. ANS: (5, 4) PTS: OBJ: NAT: TOP: KEY: 1 DIF: L2 REF: 3-1 Solving Systems Using Tables and Graphs 3-1.1 To solve a linear system using a graph or a table CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d 3-1 Problem 4 Classifying a System Without Graphing system of linear equations | inconsistent system 1 DIF: L2 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 1 Solving by Substitution system of linear equations | substitution method 1 ID: A 4. ANS: (5, 3) PTS: 1 DIF: L2 REF: 3-2 Solving Systems Algebraically OBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 3 Solving by Elimination KEY: system of linear equations | solve by elimination 5. ANS: no solutions PTS: OBJ: NAT: TOP: KEY: 6. ANS: 1 DIF: L2 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 5 Solving Systems Without Unique Solutions system of linear equations | solve by elimination | no solutions PTS: OBJ: NAT: TOP: 1 DIF: L3 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 2 Solving a System by Graphing KEY: system of inequalities | graphing 2 ID: A 7. ANS: PTS: OBJ: NAT: TOP: KEY: 8. ANS: (3, 0) PTS: OBJ: TOP: KEY: 9. ANS: (4, 5) 1 DIF: L2 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 4 Solving a Linear/Absolute-Value Systems system of inequalities | graphing | absolute value 1 DIF: L3 REF: 3-4 Linear Programming 3-4.1 To solve problems using linear programming NAT: CC A.CED.3| A.4.d 3-4 Problem 1 Testing Vertices linear programming | constraints | vertices | objective function | maximum value PTS: 1 DIF: L3 REF: 3-6 Solving Systems Using Matrices OBJ: 3-6.2 To solve a system of linear equations using matrices NAT: CC A.REI.8| A.4.d TOP: 3-6 Problem 4 Solving a System Using a Matrix KEY: systems of equations | matrices 10. ANS: (2, –2, –2) PTS: 1 DIF: L2 REF: 3-5 Systems With Three Variables OBJ: 3-5.1 To solve systems in three variables using elimination NAT: CC A.REI.6| A.4.d TOP: 3-5 Problem 1 Solving a System Using Elimination KEY: system with three variables | solve by elimination 11. ANS: (–8, –7, 5) PTS: OBJ: NAT: KEY: 1 DIF: L2 REF: 3-5 Systems With Three Variables 3-5.2 To solve systems in three variables using substitution CC A.REI.6| A.4.d TOP: 3-5 Problem 3 Solving a System Using Substitution system with three variables | substitution method 3 ID: A 12. ANS: –6 PTS: OBJ: NAT: KEY: 13. ANS: È Í Í −4 Í Í 2 Î 1 DIF: L2 REF: 3-6 Solving Systems Using Matrices 3-6.1 To represent a system of linear equations with a matrix CC A.REI.8| A.4.d TOP: 3-6 Problem 1 Identifying a Matrix Element matrix | matrix element | ˘ ˙ | ˙ ˙ ˙ −5 | 6 ˙ ˙ ˙ | ˙ ˙ ˙ | 2 ˙ −4 | ˙ ˙ ˙ ˙ ˚ PTS: 1 DIF: L4 REF: 3-6 Solving Systems Using Matrices OBJ: 3-6.1 To represent a system of linear equations with a matrix NAT: CC A.REI.8| A.4.d TOP: 3-6 Problem 2 Representing Systems With Matrices KEY: systems of equations | matrices 14. ANS: Ï Ô −2x − 9y = 11 Ì Ô 14x − 2y = 15 Ó PTS: 1 DIF: L2 REF: 3-6 Solving Systems Using Matrices OBJ: 3-6.1 To represent a system of linear equations with a matrix NAT: CC A.REI.8| A.4.d TOP: 3-6 Problem 3 Writing a System From a Matrix KEY: systems of equations | matrices 15. ANS: (–3, 1, 3) PTS: 1 DIF: L4 REF: 3-6 Solving Systems Using Matrices OBJ: 3-6.2 To solve a system of linear equations using matrices NAT: CC A.REI.8| A.4.d TOP: 3-6 Problem 5 Using a Calculator to Solve a Linear System KEY: systems of equations | matrices 16. ANS: 6 lb peanuts, 3 lb almonds, 2 lb raisins PTS: OBJ: NAT: KEY: 1 DIF: L2 REF: 3-5 Systems With Three Variables 3-5.2 To solve systems in three variables using substitution CC A.REI.6| A.4.d TOP: 3-5 Problem 4 Solving a Real-World Problem system with three variables | substitution method | word problem | problem solving 4