3-5 Solving Systems of Equations Using Cramer's Rule
Use Cramer’s Rule to solve each system of equations.
13. 4x − 5y = 39
3x + 8y = −6
ANSWER: (6, −3)
14. 5x + 6y = 20
−3x − 7y = −29
ANSWER: (−2, 5)
15. −8a − 5b = −27
7a + 6b = 22
ANSWER: (4, −1)
16. 10c − 7d = −59
6c + 5d = −63
ANSWER: (−8, −3)
17. CCSS PERSEVERANCE The ″Bermuda Triangle″ is an area located off the southeastern Atlantic coast of the United States, and noted for reports of unexplained losses of ships, small boats, and aircraft.
a. Find the area of the triangle on the map.
b. Suppose each grid represents 175 miles. What is the area of the Bermuda Triangle?
ANSWER: 2
a. 15.75 units
b. 482,343.75 mi2
Use Cramer’s Rule to solve each system of equations.
18. 4x − 2y + 7z = 26
5x + 3y − 5z = −50
−7x – 8y − 3z = 49
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ANSWER: (−3, −5, 4)
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b. Suppose each grid represents 175 miles. What is the area of the Bermuda Triangle?
ANSWER: 2
a. 15.75 Systems
units
3-5 Solving
of Equations Using Cramer's Rule
b. 482,343.75 mi2
Use Cramer’s Rule to solve each system of equations.
18. 4x − 2y + 7z = 26
5x + 3y − 5z = −50
−7x – 8y − 3z = 49
ANSWER: (−3, −5, 4)
19. −3x − 5y + 10z = −4
−8x + 2y − 3z = −91
6x + 8y − 7z = −35
ANSWER: 20. 6x − 5y + 2z = −49
−5x − 3y − 8z = −22
−3x + 8y − 5z = 55
ANSWER: (−3, 7, 2)
21. −9x + 5y + 3z = 50
7x + 8y − 2z = −60
−5x + 7y + 5z = 46
ANSWER: (−4, −2, 8)
22. x + 2y = 12
3y − 4z = 25
x + 6y + z = 20
ANSWER: (6, 3, −4)
23. 9a + 7b = −30
8b + 5c = 11
−3a + 10c = 73
ANSWER: (−1, −3, 7)
24. 2n + 3p − 4w = 20
4n − p + 5w = 13
3n + 2p + 4w = 15
ANSWER: (5, 2, −1)
25. x + y + z = 12
6x −Manual
2y − z- Powered
= 16 by Cognero
eSolutions
3x + 4y + 2z = 28
ANSWER: Page 2
4n − p + 5w = 13
3n + 2p + 4w = 15
ANSWER: 3-5 Solving
Systems of Equations Using Cramer's Rule
(5, 2, −1)
25. x + y + z = 12
6x − 2y − z = 16
3x + 4y + 2z = 28
ANSWER: (4, 0, 8)
Evaluate each determinant.
26. ANSWER: −102
27. ANSWER: 3
28. ANSWER: 83
29. ANSWER: −135
30. ANSWER: 124
31. ANSWER: −459
32. eSolutions Manual - Powered by Cognero
ANSWER: Page 3
31. ANSWER: 3-5 Solving
Systems of Equations Using Cramer's Rule
−459
32. ANSWER: 63
33. ANSWER: 0
34. ANSWER: −13
35. ANSWER: 728
36. ANSWER: −120
37. ANSWER: −952
38. TRAVEL Mr. Smith’s art class took a bus trip to an art museum. The bus averaged 65 miles per hour on the
highway and 25 miles per hour in the city. The art museum is 375 miles away from the school, and it took the class 7
hours to get there. Use Cramer’s Rule to find how many hours the bus was on the highway and how many hours it
was driving in the city.
ANSWER: 5 hours on the highway, 2 hours in the city
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Use Cramer’s Rule to solve each system of equations.
39. 6x − 5y = 73
−7x + 3y = −71
Page 4
37. ANSWER: 3-5 Solving
Systems of Equations Using Cramer's Rule
−952
38. TRAVEL Mr. Smith’s art class took a bus trip to an art museum. The bus averaged 65 miles per hour on the
highway and 25 miles per hour in the city. The art museum is 375 miles away from the school, and it took the class 7
hours to get there. Use Cramer’s Rule to find how many hours the bus was on the highway and how many hours it
was driving in the city.
ANSWER: 5 hours on the highway, 2 hours in the city
Use Cramer’s Rule to solve each system of equations.
39. 6x − 5y = 73
−7x + 3y = −71
ANSWER: (8, −5)
40. 10a − 3b = −34
3a + 8b = −28
ANSWER: (−4,−2)
41. −4c − 5d = −39
5c + 8d = 54
ANSWER: (6, 3)
42. −6f − 8g = −22
–11f + 5g = −60
ANSWER: (5, −1)
43. 9r + 4s = −55
−5r − 3s = 36
ANSWER: (−3, −7)
44. −11u − 7v = 4
9u + 4v = −24
ANSWER: (−8, 12)
45. 5x − 4y + 6z = 58
−4x + 6y + 3z = −13
6x + 3y + 7z = 53
ANSWER: (4, −2, 5)
46. 8x − 4y + 7z = 34
5x + 6y + 3z = −21
eSolutions
- Powered
3x +Manual
7y − 8z
= −85 by Cognero
ANSWER: Page 5
−4x + 6y + 3z = −13
6x + 3y + 7z = 53
ANSWER: 3-5 Solving
Systems of Equations Using Cramer's Rule
(4, −2, 5)
46. 8x − 4y + 7z = 34
5x + 6y + 3z = −21
3x + 7y − 8z = −85
ANSWER: (−3, −4, 6)
47. DOUGHNUTS Mi-Ling is ordering doughnuts for a class party. The box contains 2 dozen doughnuts, some of
which are plain and some of which are jelly-filled. The plain doughnuts each cost $0.50, and the jelly-filled cost
$0.60. If the total cost is $12.60, use Cramer’s Rule to find how many jelly-filled doughnuts Mi-Ling ordered.
ANSWER: 6
48. CCSS PERSEVERANCE The salary for each of the stars of a new movie is $5 million, and the supporting actors
each receive $1 million. The total amount spent for the salaries of the actors and actresses is $19 million. If the cast
has 7 members, use Cramer’s Rule to find the number of stars in the movie.
ANSWER: 3
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