Pre-Test Name Date 1. Determine the solution to each system of equations. a. 3x 2 y 5 5 2x 1 7y 5 212 b. 22x 5 210y 2 2 2x 1 8y 5 5 2. Determine the number of solutions for each system of equations. 4y 5 3x 2 28 4y 5 3x 1 8 b. 5y 5 25x 1 10 c. y 1 x 5 2 2y 5 x 2 y 5 2x 1 4 3. The graph shows the average attendance for two schools. What does the solution x 5 14 represent? 1400 y 1300 Average Attendance 1200 1100 1000 900 800 700 00 0 2 4 8 10 12 14 1 18 Years x Chapter Assessments 899
Pre-Test page 2 4. Tell whether each system of equations would best be solved using the substitution method or the linear combinations method. x 5 4 2 2y 8y 1 3x 5 1 b. y 1 x 5 21 5y 2 3x 5 7 c. x 2 8y 5 32 4x 1 y 5 12 5. Determine the solution to each system of equations. x 1 2y 5 2 23x 2 4y 5 213 b. 0.5x 5 0.25y 2 0.5 0.2x 1 0.75y 5.. Brittany and Lynn each earn a base salary plus commission. Brittany earns $2000 plus 15% of her sales each month. Lynn earns $2200 plus 10% of her sales each month. How much will Brittany and Lynn need to sell in order to earn the same amount each month? 900 Chapter Assessments
Post-Test Name Date 1. Determine the solution to each system of equations. y 2 2x 5 22 a. 3x 2 4y 5 8 b. 8y 5 2 9x y 1 5 5 24x 2. Determine the number of solutions for each system of equations. 2x 1 2y 5 210 b. y 1 5 5 3x 2y 2 8 5 x y 2 x 5 21 c. 10x 1 4 5 2y 3y 1 9 5 15x 3. The graph shows the total number of widgets produced by two companies. What does the solution x 5 5 represent? 1800 y 100 Number of Widgets 1400 1200 1000 800 00 400 200 0 1 2 3 4 5 7 8 9 Hours x Chapter Assessments 901
Post-Test page 2 4. Tell whether each system of equations would best be solved using the substitution method or the linear combinations method. 2y 5 9 1 x y 2 2x 5 215 b. 27 1 x 5 24y 8y 5 23x y 1 18 5 2x c. 7x 2 1 5 5y 5. Determine the solution to each system of equations. 22x 1 7y 5 13 4x 2 y 5 22 b. 0.4x 1 0.9y 5 21.9 20.8x 5 0.5 1 0.7y. Workout Plus offers a membership for $30 each month plus a $100 start up fee. Fit Works offers a membership for $50 each month plus a $20 start up fee. After how many months will memberships to both gyms cost the same amount? 902 Chapter Assessments
End of Chapter Test Name Date 1. Finest Cooks offers a membership to take cooking classes for an initial fee of $0 plus $20 for each lesson. Professional Cooks offers a membership to take cooking classes for an initial fee of $15 plus $35 for each lesson. After how many cooking classes will the cost at both companies be the same? 2. Tell whether each system of equations would best be solved using the substitution method or the linear combinations method. 25x 1 8y 5 40 y 1 3x 5 20 35 2 7x 5 5y b. 14x 1 15y 5 10 c. 9x 1 12 5 4y 8y 2 3x 5 3. Determine the solution to each system of equations. 23x 1 y 5 10 2x 2 7y 5 b. x 2 y 5 2 y 2 3x 5 220 Chapter Assessments 903
End of Chapter Test page 2 4. Determine the solution to each system of equations. 3x 5 8y 2 4 x 1 2y 5 28 b. 1 10 x 1 3 8 y 5 1 1 4 y 1 1 5 2 2 5 x 5. The graph shows the number of automobiles sold by two companies over the first five months of the year. What does the solution x 5 3 represent? 900 y Automobiles Sold 800 700 00 500 400 300 200 100 0 1 2 3 4 5 7 8 9 Months x. A sports ticketing company offers two ticket plans. One plan costs $110 plus $25 per ticket. The other plan costs $40 per ticket. How many tickets must Gloria buy in order for the first plan to be the better buy? 904 Chapter Assessments
End of Chapter Test page 3 Name Date 7. Explain when each method (graphing, substitution, linear combinations) is a good method to find a solution to a system of equations. 8. Keith and Adam are personal trainers. Keith offers personal training sessions for $35 each plus a $115 start up fee. Adam offers personal training sessions for $0 each plus a $15 start up fee. Write and graph a system of linear equations that represents this situation. Determine the number of sessions at which both trainers will cost the same amount. 900 y Cost (dollars) 800 700 00 500 400 300 200 100 0 1 2 3 4 5 7 8 9 Sessions x 9. Dawn and Claire both earn a base salary plus commission. Dawn earns $1000 plus 25% of her sales each month. Claire earns $2000 plus 10% of her sales each month. Write a system of equations that represents this situation. Let x represent the amount in sales each month. Chapter Assessments 905
End of Chapter Test page 4 10. Tell whether each system of equations would best be solved using the substitution method or the linear combinations method. Then solve the system of equations. 8x 5 3y 2 11 24x 2 5 22y b. 23x 2 1 5 2y 2x 1 y 5 2 11. Graph the system of equations. Determine the solution. 2x 5 10 2 3y 3x 1 2y 5 5 y 8 4 2 28 2 24 22 0 2 22 24 2 28 4 8 x 12. How many solutions does each system of equations have? 3x 2 y 5 1 3y 1 3 5 9x b. y 1 4x 5 7 22y 2 4 5 8x c. 4y 5 3x 1 4 8y 2 x 5 8 90 Chapter Assessments
Standardized Test Practice Name Date 1. Samuel pays $59.99 plus $0.25 for each minute over 450 minutes for his cell phone plan. Monica pays $4.99 plus $0.10 for each minute over 450 minutes for her cell phone plan. Which system of equations represents this situation? Let x represent the number of minutes over 450. y 5 59.99x 1 0.10 a. y 5 4.99x 1 0.25 y 5 59.99x 1 0.25 b. y 5 4.99x 1 0.10 y 5 59.99 1 0.10x c. y 5 4.99 1 0.25x y 5 59.99 1 0.25x d. y 5 4.99 1 0.10x 2. Which system of equations is best solved by using substitution? 2x 1 9y 5 18 5y 2 3x 5 24 x 2 2y 5 17 b. 9y 5 3x 1 4y 5 3x c. 7y 2 9x 5 224 14x 5 4y 2 5 d. 9 2 3x 5 22y 3. Solve this system of equations. 3x 1 4y 5 18 x 2 2y 5 a. (2, 3) b. (3, 2) c. (22, 23) d. (23, 22) 4. Jonathon and Raymond earn a base salary plus commission. Jonathon earns $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathon and Raymond need to sell in order to earn the same amount each month? a. $0 b. $000 c. $21,000 d. $54,000 Chapter Assessments 907
Standardized Test Practice page 2 5. Solve this system of equations. 1 5 22x 1 9y x 5 2y 1 2 a. (24, 21) b. (4, 21) c. (4, 1) d. (24, 1). Download Central offers a free membership and unlimited mp3 downloads for $25 each month. Save & Download charges $5 each month for a membership and $1 per mp3 download. How many mp3s must Grant download for the cost at both companies to be the same? a. 5 b. 15 c. 20 d. 30 7. Which would be the best method to use to solve this system of equations? 0.5x 1 0.09y 5 1. 20.03y 1 0.25x 5 0.38 a. graphing b. substitution c. linear combinations d. A solution cannot be found. 8. Solve this system of equations. 25 5 2x 1 3y 8y 5 2x 1 4 a. (21, 2) b. (2, 21) c. (1, 22) d. (22, 1) 9. Solve this system of equations. 0.2x 1 0.y 5 3. 0.4x 2 0.9y 5 21.2 a. (24, ) b. (2, 4) c. (4, ) d. (, 4) 908 Chapter Assessments
Standardized Test Practice page 3 Name Date 10. The graph shows the amount of profit for two companies. What does the solution x 5 3 represent? $900 y Profit (in thousands) $800 $700 $00 $500 $400 $300 $200 $100 0 1 2 3 4 5 7 8 9 Years x a. The two companies never have the same amount of profit. b. After three years, the companies both have $425 in profit. c. After two years, the companies both have $425,000 in profit. d. After three years, the companies both have $425,000 in profit. 11. Solve this system of equations. 24x 1 7y 5 22 2x 1 5y 5 21 a. (22, 23) b. (23, 22) c. (.5, 24) d. (2.5, 24) Chapter Assessments 909
Standardized Test Practice page 4 12. A cable company offers two movie plans. One plan costs $120 per month plus $5 per movie. The other plan costs $150 per month for unlimited movies. How many movies must Neil rent in order for the plans to cost the same amount? a. 5 b. c. 25 d. 30 13. When is graphing a system of equations a good method to determine a solution? a. when the numbers are easy to graph b. when an exact solution is needed c. when one variable can be easily isolated d. when the coefficients of like terms are multiples 14. Solve this system of equations. 22y 5 23x 2 13 2x 1 3y 5 13 a. (25, 1) b. (1, 25) c. (5, 21) d. (21, 5) 15. How many solutions does this system of equations have? y 5 7 2 4x y 5 22(2x 1 4) a. 0 b. 1 c. 2 d. infinitely many 1. Which would be the best method to use to solve this system of equations? 0.3x 1 y 5 24.8 0.5x 5 210 2 2y a. graphing b. substitution c. linear combinations d. A solution cannot be found. 910 Chapter Assessments
Standardized Test Practice page 5 Name Date 17. Solve this system of equations. 9x 2 4y 5 1 23x 1 8y 5 247 a. (3, 27) b. (23, 7) c. (23, 27) d. (27, 23) 18. Two plumbers charge different rates for service. The first plumber charges $100 per service call plus $25 per hour of service. The second plumber charges $50 per service call plus $50 per hour of service. After how many hours do the plumbers charge the same amount? a. 0 b. 1 c. 2 d. 3 19. How many solutions does this system of equations have? 2 10 5 2x y 1 2 y 5 x 1 5 a. 0 b. 1 c. 2 d. infinitely many 20. A phone company has two long distance calling plans. The first plan is $25 per month for unlimited long distance calling. The second plan is $10 per month plus $0.05 per minute of long distance calling. After how many minutes of long distance calls will it be cheaper for a customer to purchase the first plan? a. 100 b. 150 c. 300 d. 500 Chapter Assessments 911
912 Chapter Assessments