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Name Class
Date
Chapter 6 Test
Form G
Do you know HOW? Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. 1. x 2 2y 5 3
2. x 1 y 5 3
3. 2x 5 24y 1 10
y 5 22x 1 6
3x 2 2y 5 4
6y 5 23x 1 12
(3, 0); one solution
(2, 1); one solution
no solution
Solve each system using substitution. 4. 3x 2 5y 5 21
5. x 1 2y 5 21
6. 2x 1 3y 5 9
x 2 y 5 21
2x 2 3y 5 12
3x 1 4y 5 5
(22, 21)
(3, 22)
(221, 17)
7. 7x 5 2y 1 1
y 8. x 1 2 5 4 x 3 1 2y 5 5 (3, 2)
4y 5 23x 1 15 (1, 3)
y x 9. 2 1 4 5 3
2x 2 y 5 4 (4, 4)
Solve each system using elimination. 12. x 1 y 5 7
10. x 1 y 5 4
11. 22x 1 3y 5 9
x2y56
2x 2 2y 5 24
3x 2 2y 5 11
(5, 21)
(3, 5)
(5, 2)
14. 0.4x 1 0.3y 5 1.7
13. 7x 2 8y 5 11
15. 3x 2 7y 1 10 5 0
8x 2 7y 5 7
0.7x 2 0.2y 5 0.8
y 2 2x 2 3 5 0
(21.4, 22.6)
(2, 3)
(21, 1)
Write a system of equations to model each situation. Solve by any method. 16. Ten years from now, A will be twice as old as B. Five years ago, A was three
times as old as B. What are the present ages of A and B? A is 50 and B is 20 17. The ratio of incomes of two persons is 9:7. The difference in their weekly
incomes is $200. What are their weekly incomes? $900 and $700 18. A change purse contains a total of 100 nickels and dimes. The total value of the
coins is $7. How many coins of each type does the purse contain? 40 dimes and 60 nickels
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
63
Name Class
Date
Chapter 6 Test (continued)
Form G
Graph each inequality in the coordinate plane. 20. 2x 2 y $ 1
19. 2x 1 3y # 6 y
21. 23x 1 2y , 5
y
4
y
4
2
4
2
2
x
−4 −2
2
O
x
−4 −2
4
2
O
x
−4 −2
4
2
O
−2
−2
−2
−4
−4
−4
4
Solve each system of inequalities by graphing. 22. 2x 1 3y # 6
HSM11A1TR_0606_ANT030 3x 1 2y # 6
23. x 1 y $ 9
3x 1 y $ 12
y
18
4
2x 1 y , 15
y
2
y
36 24
6
x O
24. 5x 1 y . 10
HSM11A1TR_0606_ANT032
12
2 −4 −2
HSM11A1TR_0606_ANT031
12 x
x
4
−12 −6
−2 −4
O
6
12
18
−8 −4
O
−6
−12
−12
−24
25. For a party, you can spend no more than $20 on cakes. Egg cake
cost $4 and cream cake cost $2. Write the linear inequality that models the situation. GraphHSM11A1TR_0606_ANT034 the inequality. 4x 1 2y K 20
HSM11A1TR_0606_ANT033
10 9 8 7 6 5 4 3 2 1
4
8
10
y
HSM11A1TR_0606_ANT035
Do you UNDERSTAND?
O
x
2
4
6
8
10
26. Open-Ended Write a system of linear equations that has infinitely many
solutions. Answers may vary. Sample: y 5 2x 2 5; 24x 1 2y 5 210
HSM11A1TR_0606_ANT036
27. Error Analysis A student determined that (1, 1) is one of the solutions of the
linear inequality y # 2x 2 3, as shown below. What error did the student make?
y # 2x 2 3
1 # 2(1) 2 3
1#1 When the student simplified the expression 2(1) 23, the student got 1 instead of 21.
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
64
Name Class
Date
Chapter 6 Test
Form K
Do you know HOW? Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. 1 1. y 5 2 x 1 4
2. y 5 x 1 2
3. x 1 y 5 2
y 5 22x 2 1
y 5 3x 1 6
x 1 y 5 21
(22, 3); one solution
(22, 0); one solution
no solution
Solve each system using substitution. 4. x 1 y 5 1
5. x 2 4y 5 11
6. 2x 1 y 5 1
2x 1 3y 5 24
2y 2 x 5 27
x 2 2y 5 23
(7, 26)
(3, 22)
(5, 29)
Solve each system using elimination. 7. 2x 1 3y 5 10
8. x 1 y 5 26
9. 3x 5 22y 2 5
2x 2 y 5 214
x2y56
2y 5 25x 1 5
(24, 6)
(0, 26)
(5, 210)
Solve each problem. 10. The sum of two numbers is 23. If one of the numbers is halved, the sum will
become 17. What are the numbers? 11 and 12 11. The perimeter of a rectangle is 60 cm. The length is four times the width. What
are the length and the width of the rectangle? length 5 24 cm; width 5 6 cm
Write a system of equations to model each situation. Solve by any method. 12. Sarah is 25 years older than her son Gavin. In ten years, Sarah will be twice
Gavin’s age. How old are Sarah and Gavin now? Sarah 5 40 yr; Gavin 5 15 yr 13. A chemist is mixing a solution that is 2% acid and another solution that is 8%
acid. She needs to make 75 mL of a solution that is 5% acid. How much of each solution should she use? 37.5 mL of the 2% solution and 37.5 mL of the 8% solution
Prentice Hall Foundations Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
67
Name Class
Date
Chapter 6 Test (continued)
Form K
Graph each inequality in the coordinate plane. 14. x 1 2y # 10
15. 4x 2 2y $ 3
y
8
y
8 4
4
x
x
−8 −4
4
O
−8 −4
8
4
O
−4
−4
−8
−8
8
Solve each system of inequalities by graphing. 16. 4x 1 y $ 1
17. x 1 4y . 22
y
y
8 HSM11A1TR_TEST_B_T006705 5x 1 3y , 7 4
8 HSM11A1TR_TEST_B_T006704 3x 2 y # 6 4
x
x
−8 −4
O
4
−8 −4
8
4
O
−4
−4
−8
−8
18. For a work banquet, Jack can spend no more than $200 on dessert.
Fruit pies cost $9 each and cakes cost $20 each. Write the linear inequality that models the situation. Graph the inequality.
8
y
10 8 6
9xHSM11A1TR_TEST_B_T006710 1 20y K 200 4
HSM11A1TR_TEST_B_T006709
2 x O
2
4
6
8
10
Do you UNDERSTAND? 19. Writing How do you check to see if an ordered pair satisfies a system of
HSM11A1TR_TEST_B_T006803
inequalities graphically? You can plot the point on the graph and see if it lies within the shaded region.
20. Open-Ended Write a system of inequalities in which the shaded region is
below both lines. Graph the system. Answers may vary. Sample: yKx12 y R 2x 2 1
y
8 4 x
−8 −4
O
4
8
−4 −8
21. Open-Ended Write a system of linear equations that has no solution. Answers may vary. Sample: y 5 3x 1 5 y 5 3x 2 1 HSM11A1TR_TEST_B_T006802 Prentice Hall Foundations Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
68
Date
Chapter 6 Test
Form G
Do you know HOW? Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. 1. x 2 2y 5 3
2. x 1 y 5 3
3. 2x 5 24y 1 10
y 5 22x 1 6
3x 2 2y 5 4
6y 5 23x 1 12
(3, 0); one solution
(2, 1); one solution
no solution
Solve each system using substitution. 4. 3x 2 5y 5 21
5. x 1 2y 5 21
6. 2x 1 3y 5 9
x 2 y 5 21
2x 2 3y 5 12
3x 1 4y 5 5
(22, 21)
(3, 22)
(221, 17)
7. 7x 5 2y 1 1
y 8. x 1 2 5 4 x 3 1 2y 5 5 (3, 2)
4y 5 23x 1 15 (1, 3)
y x 9. 2 1 4 5 3
2x 2 y 5 4 (4, 4)
Solve each system using elimination. 12. x 1 y 5 7
10. x 1 y 5 4
11. 22x 1 3y 5 9
x2y56
2x 2 2y 5 24
3x 2 2y 5 11
(5, 21)
(3, 5)
(5, 2)
14. 0.4x 1 0.3y 5 1.7
13. 7x 2 8y 5 11
15. 3x 2 7y 1 10 5 0
8x 2 7y 5 7
0.7x 2 0.2y 5 0.8
y 2 2x 2 3 5 0
(21.4, 22.6)
(2, 3)
(21, 1)
Write a system of equations to model each situation. Solve by any method. 16. Ten years from now, A will be twice as old as B. Five years ago, A was three
times as old as B. What are the present ages of A and B? A is 50 and B is 20 17. The ratio of incomes of two persons is 9:7. The difference in their weekly
incomes is $200. What are their weekly incomes? $900 and $700 18. A change purse contains a total of 100 nickels and dimes. The total value of the
coins is $7. How many coins of each type does the purse contain? 40 dimes and 60 nickels
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
63
Name Class
Date
Chapter 6 Test (continued)
Form G
Graph each inequality in the coordinate plane. 20. 2x 2 y $ 1
19. 2x 1 3y # 6 y
21. 23x 1 2y , 5
y
4
y
4
2
4
2
2
x
−4 −2
2
O
x
−4 −2
4
2
O
x
−4 −2
4
2
O
−2
−2
−2
−4
−4
−4
4
Solve each system of inequalities by graphing. 22. 2x 1 3y # 6
HSM11A1TR_0606_ANT030 3x 1 2y # 6
23. x 1 y $ 9
3x 1 y $ 12
y
18
4
2x 1 y , 15
y
2
y
36 24
6
x O
24. 5x 1 y . 10
HSM11A1TR_0606_ANT032
12
2 −4 −2
HSM11A1TR_0606_ANT031
12 x
x
4
−12 −6
−2 −4
O
6
12
18
−8 −4
O
−6
−12
−12
−24
25. For a party, you can spend no more than $20 on cakes. Egg cake
cost $4 and cream cake cost $2. Write the linear inequality that models the situation. GraphHSM11A1TR_0606_ANT034 the inequality. 4x 1 2y K 20
HSM11A1TR_0606_ANT033
10 9 8 7 6 5 4 3 2 1
4
8
10
y
HSM11A1TR_0606_ANT035
Do you UNDERSTAND?
O
x
2
4
6
8
10
26. Open-Ended Write a system of linear equations that has infinitely many
solutions. Answers may vary. Sample: y 5 2x 2 5; 24x 1 2y 5 210
HSM11A1TR_0606_ANT036
27. Error Analysis A student determined that (1, 1) is one of the solutions of the
linear inequality y # 2x 2 3, as shown below. What error did the student make?
y # 2x 2 3
1 # 2(1) 2 3
1#1 When the student simplified the expression 2(1) 23, the student got 1 instead of 21.
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
64
Name Class
Date
Chapter 6 Test
Form K
Do you know HOW? Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. 1 1. y 5 2 x 1 4
2. y 5 x 1 2
3. x 1 y 5 2
y 5 22x 2 1
y 5 3x 1 6
x 1 y 5 21
(22, 3); one solution
(22, 0); one solution
no solution
Solve each system using substitution. 4. x 1 y 5 1
5. x 2 4y 5 11
6. 2x 1 y 5 1
2x 1 3y 5 24
2y 2 x 5 27
x 2 2y 5 23
(7, 26)
(3, 22)
(5, 29)
Solve each system using elimination. 7. 2x 1 3y 5 10
8. x 1 y 5 26
9. 3x 5 22y 2 5
2x 2 y 5 214
x2y56
2y 5 25x 1 5
(24, 6)
(0, 26)
(5, 210)
Solve each problem. 10. The sum of two numbers is 23. If one of the numbers is halved, the sum will
become 17. What are the numbers? 11 and 12 11. The perimeter of a rectangle is 60 cm. The length is four times the width. What
are the length and the width of the rectangle? length 5 24 cm; width 5 6 cm
Write a system of equations to model each situation. Solve by any method. 12. Sarah is 25 years older than her son Gavin. In ten years, Sarah will be twice
Gavin’s age. How old are Sarah and Gavin now? Sarah 5 40 yr; Gavin 5 15 yr 13. A chemist is mixing a solution that is 2% acid and another solution that is 8%
acid. She needs to make 75 mL of a solution that is 5% acid. How much of each solution should she use? 37.5 mL of the 2% solution and 37.5 mL of the 8% solution
Prentice Hall Foundations Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
67
Name Class
Date
Chapter 6 Test (continued)
Form K
Graph each inequality in the coordinate plane. 14. x 1 2y # 10
15. 4x 2 2y $ 3
y
8
y
8 4
4
x
x
−8 −4
4
O
−8 −4
8
4
O
−4
−4
−8
−8
8
Solve each system of inequalities by graphing. 16. 4x 1 y $ 1
17. x 1 4y . 22
y
y
8 HSM11A1TR_TEST_B_T006705 5x 1 3y , 7 4
8 HSM11A1TR_TEST_B_T006704 3x 2 y # 6 4
x
x
−8 −4
O
4
−8 −4
8
4
O
−4
−4
−8
−8
18. For a work banquet, Jack can spend no more than $200 on dessert.
Fruit pies cost $9 each and cakes cost $20 each. Write the linear inequality that models the situation. Graph the inequality.
8
y
10 8 6
9xHSM11A1TR_TEST_B_T006710 1 20y K 200 4
HSM11A1TR_TEST_B_T006709
2 x O
2
4
6
8
10
Do you UNDERSTAND? 19. Writing How do you check to see if an ordered pair satisfies a system of
HSM11A1TR_TEST_B_T006803
inequalities graphically? You can plot the point on the graph and see if it lies within the shaded region.
20. Open-Ended Write a system of inequalities in which the shaded region is
below both lines. Graph the system. Answers may vary. Sample: yKx12 y R 2x 2 1
y
8 4 x
−8 −4
O
4
8
−4 −8
21. Open-Ended Write a system of linear equations that has no solution. Answers may vary. Sample: y 5 3x 1 5 y 5 3x 2 1 HSM11A1TR_TEST_B_T006802 Prentice Hall Foundations Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its s. All Rights Reserved.
68
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