Download State whether each sentence is true or false. If false, replace the

Study Guide and Review - Chapter 6
State whether each sentence is true or false. If false, replace the underlined term to make a true
sentence.
1. If a system has at least one solution, it is said to be consistent.
ANSWER: true
2. If a consistent system has exactly two solution(s), it is said to be independent.
ANSWER: false; one
3. If a consistent system has an infinite number of solutions, it is said to be inconsistent.
ANSWER: false; dependent
4. If a system has no solution, it is said to be inconsistent.
ANSWER: true
5. Substitution involves substituting an expression from one equation for a variable in the other.
ANSWER: true
6. In some cases, dividing two equations in a system together will eliminate one of the variables. This process is called
elimination.
ANSWER: false; adding or subtracting
7. A set of two or more inequalities with the same variables is called a system of equations.
ANSWER: false; system of inequalities
8. When the graphs of the inequalities in a system of inequalities do not intersect, there are no solutions to the system.
ANSWER: true
Graph each system and determine the number of solutions that it has. If it has one solution, name it.
9. x − y = 1
x +y = 5
ANSWER: one; (3, 2)
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false; system of inequalities
8. When the graphs of the inequalities in a system of inequalities do not intersect, there are no solutions to the system.
ANSWER: Study
Guide and Review - Chapter 6
true
Graph each system and determine the number of solutions that it has. If it has one solution, name it.
9. x − y = 1
x +y = 5
ANSWER: one; (3, 2)
10. y = 2x − 4
4x + y = 2
ANSWER: one; (1, −2)
11. 2x − 3y = −6
y = −3x + 2
ANSWER: one; (0, 2)
12. −3x + y = −3
y = xManual
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ANSWER: one; (0, −3)
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Study Guide and Review - Chapter 6
12. −3x + y = −3
y =x−3
ANSWER: one; (0, −3)
13. x + 2y = 6
3x + 6y = 8
ANSWER: no solution
14. 3x + y = 5
6x = 10 − 2y
ANSWER: infinitely many solutions
15. MAGIC NUMBERS Sean is trying to find two numbers with a sum of 14 and a difference of 4. Define two
variables, write a system of equations, and solve by graphing.
ANSWER: Sample answer: Let x be one number and y the other number; x + y = 14; x − y = 4; 9 and 5
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Study Guide and Review - Chapter 6
15. MAGIC NUMBERS Sean is trying to find two numbers with a sum of 14 and a difference of 4. Define two
variables, write a system of equations, and solve by graphing.
ANSWER: Sample answer: Let x be one number and y the other number; x + y = 14; x − y = 4; 9 and 5
Use substitution to solve each system of equations.
16. x + y = 3
x = 2y
ANSWER: (2, 1)
17. x + 3y = −28
y = −5x
ANSWER: (2, −10)
18. 3x + 2y = 16
x = 3y − 2
ANSWER: (4, 2)
19. x − y = 8
y = −3x
ANSWER: (2, −6)
20. y = 5x − 3
x + 2y = 27
ANSWER: (3, 12)
21. x + 3y = 9
x +y = 1
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(−3, Manual
4)
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22. GEOMETRY The perimeter of a rectangle is 48 inches. The length is 6 inches greater than the width. Define the
20. y = 5x − 3
x + 2y = 27
ANSWER: Study
Guide and Review - Chapter 6
(3, 12)
21. x + 3y = 9
x +y = 1
ANSWER: (−3, 4)
22. GEOMETRY The perimeter of a rectangle is 48 inches. The length is 6 inches greater than the width. Define the
variables, and write equations to represent this situation. Solve the system by using substitution.
ANSWER: Sample answer: Let w be the width and l be the length; 2l + 2w = 48, l = w + 6; 9 is the width and 15 is the length.
Use elimination to solve each system of equations.
23. x + y = 13
x −y = 5
ANSWER: (9, 4)
24. −3x + 4y = 21
3x + 3y = 14
ANSWER: 25. x + 4y = −4
x + 10y = −16
ANSWER: (4, −2)
26. 2x + y = −5
x −y = 2
ANSWER: (−1, −3)
27. 6x + y = 9
−6x + 3y = 15
ANSWER: 28. x − 4y = 2
3x + 4y = 38
ANSWER: (10, 2)
29. 2x + 2y = 4
2x − 8y = −46
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ANSWER: (−3, 5)
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28. x − 4y = 2
3x + 4y = 38
ANSWER: Study
Guide and Review - Chapter 6
(10, 2)
29. 2x + 2y = 4
2x − 8y = −46
ANSWER: (−3, 5)
30. 3x + 2y = 8
x + 2y = 2
ANSWER: 31. BASEBALL CARDS Cristiano bought 24 baseball cards for $50. One type cost $1 per card, and the other cost $3
per card. Define the variables, and write equations to find the number of each type of card he bought. Solve by using
elimination.
ANSWER: Sample answer: Let f be the number of the first type of card, and let c be the number of the second type of card; f + c =
24, f + 3c = 50; 11 $1 cards and 13 $3 cards.
Use elimination to solve each system of equations.
32. x + y = 4
−2x + 3y = 7
ANSWER: (1, 3)
33. x − y = −2
2x + 4y = 38
ANSWER: (5, 7)
34. 3x + 4y = 1
5x + 2y = 11
ANSWER: (3, −2)
35. −9x + 3y = −3
3x − 2y = −4
ANSWER: (2, 5)
36. 8x − 3y = −35
3x + 4y = 33
ANSWER: (−1, 9)
37. 2x + 9y = 3
5x + 4y = 26
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ANSWER: (6, −1)
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36. 8x − 3y = −35
3x + 4y = 33
ANSWER: Study
Guide and Review - Chapter 6
(−1, 9)
37. 2x + 9y = 3
5x + 4y = 26
ANSWER: (6, −1)
38. −7x + 3y = 12
2x − 8y = −32
ANSWER: (0, 4)
39. 8x − 5y = 18
6x + 6y = −6
ANSWER: (1, −2)
40. BAKE SALE On the first day, a total of 40 items were sold for $356. Define the variables, and write a system of
equations to find the number of cakes and pies sold. Solve by using elimination.
ANSWER: Sample answer: Let c represent the number of the cakes, and let p represent the number of pies; 8c + 10p = 356, p
+ c = 40; 22 cakes, 18 pies
Determine the best method to solve each system of equations. Then solve the system.
41. y = x − 8
y = −3x
ANSWER: Subs.;
(2, −6)
42. y = −x
y = 2x
ANSWER: Subs.;
(0, 0)
43. x + 3y = 12
x = −6y
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ANSWER: Subs.;
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y = 2x
ANSWER: Subs.;
Study
Guide and Review - Chapter 6
(0, 0)
43. x + 3y = 12
x = −6y
ANSWER: Subs.;
(24, −4)
44. x + y = 10
x − y = 18
ANSWER: Elim (+); (14, −4)
45. 3x + 2y = −4
5x + 2y = −8
ANSWER: Elim (–);
(−2, 1)
46. 6x + 5y = 9
−2x + 4y = 14
ANSWER: Elim (×);
(−1, 3)
47. 3x + 4y = 26
2x + 3y = 19
ANSWER: Elim (×);
(2, 5)
48. 11x − 6y = 3
5x − 8y = −25
ANSWER: Elim (×);
(3, 5)
49. COINS Tionna has 25 coins in her piggy bank with a value of $4. The coins are either dimes or quarters. Define
the variables, and write a system of equations to determine the number of dimes and quarters. Then solve the system
using the best method for the situation.
ANSWER: Sample answer: Let d represent the number of dimes and let q represent the number of quarters; d + q = 25, 0.10d
+ 0.25q = 4; 15 dimes, 10 quarters
50. FAIR At a county fair, the cost for 4 slices of pizza and 2 orders of French fries is $21.00. The cost of 2 slices of
pizza and 3 orders of French fries is $16.50. To find out how much a single slice of pizza and an order of French
fries costs, define the variables and write a system of equations to represent the situation. Determine the best
method to solve the system of equations. Then solve the system.
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Let p represent the cost of a slice of pizza and t represent the cost of an order of French fries; 4p + 2f = 21, 2p + 3f
= 16.5; Sample answer: elimination; pizza $3.75; French fries $3.
using the best method for the situation.
ANSWER: Sample
Let d represent
Study
Guideanswer:
and Review
- Chapterthe6 number of dimes and let q represent the number of quarters; d + q = 25, 0.10d
+ 0.25q = 4; 15 dimes, 10 quarters
50. FAIR At a county fair, the cost for 4 slices of pizza and 2 orders of French fries is $21.00. The cost of 2 slices of
pizza and 3 orders of French fries is $16.50. To find out how much a single slice of pizza and an order of French
fries costs, define the variables and write a system of equations to represent the situation. Determine the best
method to solve the system of equations. Then solve the system.
ANSWER: Let p represent the cost of a slice of pizza and t represent the cost of an order of French fries; 4p + 2f = 21, 2p + 3f
= 16.5; Sample answer: elimination; pizza $3.75; French fries $3.
Solve each system of inequalities by graphing.
51. x > 3
y <x+2
ANSWER: 52. y ≤ 5
y >x−4
ANSWER: 53. y < 3x − 1
y ≥ −2x + 4
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Guide and Review - Chapter 6
Study
53. y < 3x − 1
y ≥ −2x + 4
ANSWER: 54. y ≤ −x − 3
y ≥ 3x − 2
ANSWER: 55. JOBS Kishi makes $7 an hour working at the grocery store and $10 an hour delivering newspapers. She cannot
work more than 20 hours per week. Graph two inequalities that Kishi can use to determine how many hours she
needs to work at each job if she wants to earn at least $90 per week.
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