Fala, pessoal!
Segue uma lista para encontrar o encontro entre duas retas, se existir.
Q01. Determine, se existir, a intersecção entre as duas retas:
Determine a intersecção das retas:
1. 7x + 5y = 8, −3x + (−2)y = −6
2. −5x − 7y = −3, −4x + (−6)y = 1
3. 7x − (−y) = −6, −x − 0y = −6
4. 6x − (−y) = −6, −6x − y = −1
5. −4x − (−9)y = −8, 20x − 45y = −32
6. −2x + (−3)y = 5, x − (−y) = −14
7. −2x + (−7)y = −12, 2x + 6y = 13
8. −x − (−7)y = −1, 2x − 16y = −12
9. −5x + 3y = 8, x + (−y) = −1
10. x + (−3)y = 4, −5x + 16y = 7
11. 3x − 2y = −11, −2x + 2y = 3
12. x − (−2)y = 13, −x − 0y = 14
13. −6x − (−7)y = −2, −2x + 2y = 13
14. −7x − 5y = 11, −4x + (−3)y = −13
15. 5x − (−6)y = 5, 25x + 30y = 4
16. 2x − (−5)y = −5, −6x − 14y = −4
17. −2x − 7y = 1, 2x + 6y = 13
18. −x + 6y = −1, 2x − 13y = −6
19. −x + (−7)y = 3, −4x − 30y = −13
20. 3x − 7y = 11, −5x + 12y = −11
21. −9x + 9y = 27, −2x − (−2)y = 0
22. −x − (−5)y = −8, −6x + 28y = 8
23. −x + (−4)y = −5, −2x − 9y = −6
24. −x − (−7)y = 9, −3x − (−20)y = 11
25. −7x − 10y = 2, 14x − (−20)y = −4
26. −x − y = −4, 4x + 2y = 8
27. x − 3y = 10, −4x + 14y = 13
28. 2x + (−6)y = 4, 7x − 20y = −5
29. 6x − (−7)y = −2, −7x − 8y = 14
30. x − (−3)y = 12, −x + (−2)y = −14
31. −x − 5y = 10, 3x + 13y = −2
32. x − 8y = 5, −5x −
(−40)y = −25
33. −3x − (−5)y = −6, −x + y = −4
34. −6x + 2y = 11,
−4x − (−y) = 8
35. 4x − 2y = −6, 3x + (−y) = 3
36. 8x + (−8)y = 0, 3x − 3y = 7
37. 2x + 5y = 12, −5x + (−12)y = 5
38. −4x − 2y = 8, 7x
− (−3)y = −6
39. −x − (−5)y = 2, −4x + 19y = 8
40. −2x + 7y = −6, 7x − 25y = −9
41. −4x + 2y = 4, −7x − (−3)y = −7
42. 2x − (−4)y = 5, −2x + (−3)y = 12
43. −6x + (−5)y = −2, −6x + (−5)y = −6
44. −x + 5y = −4, −4x + 19y = 8
45. x + 6y = −2, −4x + (−22)y = −6
46. −5x − y = −2, −3x − y = −11
47. 5x + 9y = −2, −25x + (−45)y = 10
48. −x + 7y = 3, −3x − (−19)y = 14
49. 2x + (−2)y = 14,
−2x − (−3)y = −9
50. −2x − (−3)y = 4, −x + y = 11
51. −x − 4y = 7, −5x + (−21)y = 11
52. −2x − y = −2, 4x + y = 3
53. 2x − (−6)y = −6, −4x − 11y = 7
54. −7x − (−6)y = 8, −6x + 5y = −3
55. x + (−3)y = 3, −3x + 10y = −11
56. −6x + (−y) = 0, 30x + 5y = 0
57. 5x + 3y = −9, −7x − 4y = −8
58. −x − (−8)y = 2, x
+ (−8)y = 20
59. −2x − (−2)y = −11, −3x + 2y = 13
60. x − (−4)y = 15, −x − 3y = 7
61. 7x + 6y = −7, −6x − 5y = −8
62. 6x − 7y = −11, 2x + (−2)y = −2
63. −2x − 5y = 0, 2x + 5y = −22
64. 5x − (−8)y = −5, 25x − (−40)y = −25
65. −10x − (−6)y = −12, 15x − 9y = 18
66. −6x − (−7)y = 7, −7x + 8y = 9
67. −2x − (−y) = −6, −4x + y = −7
68. −x − 5y = −3, 4x
− (−19)y = 12
69. −x + 5y = 4, 7x + (−36)y = −11
70. −3x + y = 7, −5x
− (−y) = 9
71. x − (−3)y = −13,
2x − (−8)y = 7
72. −7x + 4y = 12, −2x + y = −2
73. 2x + 5y = −4, −2x + (−4)y = 15
74. −2x + 4y = 13, −5x − (−9)y = 5
75. 2x − 5y = −15, −6x + 16y = 3
76. x + (−y) = 5, 2x − y = 13
77. 3x + 8y = −5, −9x
− 24y = 15
78. 2x − 2y = −8, 3x − 2y = 1
79. 2x − y = −11, 3x + (−y) = 7
80. −5x − (−y) = −6, −7x + y = −4
81. x − (−6)y = −14, 5x − (−31)y = −4
82. −x + (−7)y = 10, 7x + 48y = 6
83. 4x + (−5)y = −8, x − y = 3
84. −x − 5y = −2, x −
(−3)y = −13
85. x − (−y) = 12, −3x + (−y) = −5
86. 4x − y = 5, −7x − (−2)y = 2
87. −2x + (−2)y = 3, 3x − (−2)y = 10
88. −2x + 6y = 14, −3x − (−8)y = 3
89. 3x + 5y = −8, 4x + 7y = −3
90. −x + 5y = 14, −5x + 24y = −11
91. −6x + 5y = 10, 7x
− 6y = 4
92. −x − 7y = 11, 2x + 13y = 10
93. x + 4y = 6, 2x + 9y = 15
94. −6x − (−y) = −13, −x − 0y = −15
95. 7x − 7y = 56, −2x
+ 2y = −13
96. 8x − (−6)y = 14, −4x + (−3)y = −7
97. −4x + 3y = −11, 6x + (−5)y = 14
98. x + 4y = 5, −6x + (−22)y = −15
99. −8x + 9y = −1, −24x − (−27)y = −13
100. −x + (−2)y = 9, x + y = −1
SOLUÇÕES:
1. x = 14, y = −18
2. x = 25/2 , y = −17/2
3. x = 6, y = −48
4. Nenhuma, são retas paralelas.
5. Nenhuma, são retas paralelas.
6. x = −37, y = 23
7. x = 19 2 , y = −1
8. x = 50, y = 7
9. x = −5 2 , y = −3/2
10. x = 85, y = 27
11. x = −8, y = −13/2
12. x = −14, y = 27/2
13. x = −95/2 , y = −41
14. x = −98, y = 135
15. Nenhuma, são retas paralelas.
16. x = 45, y = −19
17. x = 97/2 , y = −14
18. x = 49, y = 8
19. x = −181/2 , y = 25/2
20. x = 55, y = 22
21. Nenhuma, são retas paralelas.
22. x = −132, y = −28
23. x = 21, y = −4
24. x = 103, y = 16
25. São coincidentes.
26. x = 0, y = 4
27. x = 179/2 , y = 53/2
28. x = −55, y = −19
29. x = −82, y = 70
30. x = 18, y = −2
31. x = 60, y = −14
32. São coincidentes.
33. x = 7, y = 3
34. x = −5/2 , y = −2
35. x = 6, y = 15
36. Nenhuma, são retas paralelas.
37. x = −169, y = 70
38. x = 6, y = −16
39. x = −2, y = 0
40. x = 213, y = 60
41. x = 13, y = 28
42. x = −63/2 , y = 17
43. Nenhuma, são retas paralelas.
44. x = −116, y = −24
45. x = 40, y = −7
46. x = −9/2 , y = 49/2
47. São coincidentes.
48. x = −41/2 , y = −5/2
49. x = 12, y = 5
50. x = −29, y = −18
51. x = −103, y = 24
52. x = 1/2 , y = 1
53. x = 12, y = −5
54. x = 58, y = 69
55. x = −3, y = −2
56. São coincidentes.
57. x = 60, y = −103
58. Nenhuma, são retas paralelas.
59. x = −24, y = −59/2
60. x = −73, y = 22
61. x = 83, y = −98
62. x = 4, y = 5
63. Nenhuma, são retas paralelas.
64. São coincidentes.
65. São coincidentes.
66. x = −7, y = −5
67. x = 1/2 , y = −5
68. x = 3, y = 0
69. x = −89, y = −17
70. x = −1, y = 4
71. x = −125/2 , y = 33/2
72. x = 20, y = 38
73. x = −59/2 , y = 11
74. x = 97/2 , y = 55/2
75. x = −225/2 , y = −42
76. x = 8, y = 3
77. São coincidentes.
78. x = 9, y = 13
79. x = 18, y = 47
80. x = −1, y = −11
81. x = −410, y = 66
82. x = 522, y = −76
83. x = 23, y = 20
84. x = −71/2 , y = 15/2
85. x = −7/2 , y = 31/2
86. x = 12, y = 43
87. x = 13, y = −29/2
88. x = 47, y = 18
89. x = −41, y = 23
90. x = 391, y = 81
91. x = −80, y = −94
92. x = 213, y = −32
93. x = −6, y = 3
94. x = 15, y = 77
95. Nenhuma, são retas paralelas.
96. São coincidentes.
97. x = 13/2 , y = 5
98. x = −25, y = 15/2
99. Nenhuma, são retas paralelas.
100. x = 7, y = −8
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