Latihan Simultaneous Equation

SIMULTANEOUS EQUATION _ 02 SE 02

Solve each of the following pairs of simultaneous equations.1. x – y = 2 ; x2 – 5xy + 2y2 = 8 [ x = 1 , y = 1 ; x = 0 , y = 2 ]

2. 3x + y = 8 ; 3x2 + y2 = 28 [ x = 1 ,y = 5 ; x = 3 , y = 1 ]

3 x 2y = 7 ; x2 + 4y2 = 37 [ x = 6 ,y = ½ ; x = 1 , y = 3 ]

4. 2y – x = 1 ; xy + x2 = 26[ x = -13/3 ,y = 5/3 ; x = 4 , y = 5/2 ]

5. x – 3y = 4 ; 2x2 – 9y2 = 17 [ x = 3 ,y = 1/3 ; x = - 11, y = 5 ]

6. 2x – y = 3 ; 2x2 + 3xy = 1 [ x = 1/8 ,y = 11/4 ; x = 1 , y = 1 ]

7. x2 – y + y2 = 2x +2y = 10 [ x = 5/2 ,y = 5/2 ; x = 2 , y = 3 ]

8. x + y = 6 ;

[ x = 1 ,y = 5 ; x = 4 , y = 2 ]


Solve each of the following pairs of simultaneous equations.

9. x 2y = 3 ;

[ x = 2 ,y = ½ ; x = ½ , y = 5/3 ]

10. x + y = 7 ;

[ x = 2 ,y = 5 ; x = 14/5 , y = 21/5 ]

11. 2x 5y = 7 ; 12x2 – 5y2 = 7 [ x = 1 ,y = 1 ; x = 3/2 , y = 2 ]

12. 2x + 3y = 1 ; x(x + y) = 10 [ x = 5 ,y = 3 ; x = 6 , y = 13/3 ]

13. 2x + 3y = 7 ; x2 + xy + y2 = 7 [ x = 1 ,y = 3 ; x = 2 , y = 1 ]

14. 2x + 3y + 1 = 0 ; x2 + 6xy + 5 = 0 [ x = 1 ,y = 1 ; x = 5/3 , y = 7/9 ]

15. xy = 4 ; 2x + 3y = 14 [ x = 1 ,y = 4 ; x = 6 , y = 2/3 ]

16. k h = 2 ; k2 + 2h2 = 9 (3 decimal places) [ x = 0.742 ,y = 2.742 ; x = 6.742 , y = 4.742 ]


Solve each of the following pairs of simultaneous equations.17. [x = 1, y= 2 or x=4, y=10]

18.

[x=1, y=1/2 or x=2, y=2]

19. and Give your answers correct to two decimal places. [ x=2.81, y=1.27 or x=0.47, y=0.18]

20. Solve the simultaneous equations k – 2h = 4 and k2 – 3h = 8. Give your answers correct to three decimal places.

[ h = 0.467 . k = 3.066 ; h =4.283 , k = 4.566 ]

21. and y2 – 17 = 3x

[ x = 1/3 , y = 4 ; x = 8/3 y = 5 ]

22. 6x – 3y = x2 – x – y = 15 [ x = 5, y = 5 ; x = 2 , y = 9 ]


23. x – 2y + 9 = 0 ; x2 + xy – 27 = 0 [ x = 3 , y = 6 ; x = 6, y = 3/2 ]

24 x – 2y + 3 = 0 , x2 – xy – 5 = 0 [ x = 2 , y = ½ ; x = 5 , y = 4 ]

25. Solve simultaneous equation 3x – y = 4 and 2x2 + y2 + xy = 6 . Give your answers corrected to three decimal places. [ x = 1.535 , y = 0.605 ; x = 0.466 , y = 2.602 ]

26. Solve the simultaneous equations : 2x + 5y = x2 + 3xy – y2 = 3 [ x = 7/3 , y =1/3 ; x = 4 , y = 1 ]

27. Solve the simultaneous equations : 2x + 5y = x2 + 3xy – y2 = 3 [ x = 7/3 , y = 1/3 ; x = 4 , y =1 ]

28. Solve the simultaneous equations 4x + y + 8 = x2 + x – y = 2 [ x = 1 , y = 2 ; x = 4 , y = 10 ]

29. 4x + 2y = x2 + xy 4x = 2

[ x = 1,y= 3 , x = 2 , y = 5 ]


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30. Solve the simultaneous equation and . Give your answers correct to three decimal places. [SPM 2004] [Ans: m=0.606, p=2.606 or m=-6.606, p= 4.606] 31. Solve the simultaneous equation

and

[SPM 2005] [Ans: x=3, y=4 or x=1/2, y= 3] 32. Solve the simultaneous equation and . Give your answers correct to three decimal places.

[SPM 2006] [Ans: x=1.443, y=1.886 or z=0.693, y=2.386]

33. Solve the following simultaneous equations: ,

[SPM 2007] [Ans: x=3, y=3 or x=1, y=1]

34. Solve the following simultaneous equations: , [SPM 2008]

[Ans: x=5, y=3 or x=6, y=2/3]

35. Solve the simultaneous equations k – 3p = – 1 and p + pk – 2k = 0 [ SPM 2009 ] Give your answers correct to three decimal places.

[ p = 1.577, k = 3.731 ; p=0.423 , k = 0.268 ]


36. Find the points of intersection between the curve y2 – 2x = 13 and the straight line x – y = 1 . [ (2, 3), (5, 6) ]

37. If (3,1) is one of the solution of simultaneous equation mx – 3y = 15 and 8x2 – 27y2 = 5n , find the value of m and n . Hence, find the other solution .

[m = 4, n = 9 ]

38. The straight line y = 2x + 3 intersect the curve xy + 20 = 5y at point A and point B .

Calculate the coordinates of point A and B.

39. Given that (3k, 2p) is a solution of the simultaneous equations x – 2y = 4 and

. Find the value of k and p .

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SIMULTANEOUS EQUATION _ 08 SE 08 Solve the following simultaneous equations.

40. 2x + y = 1 ; 5x2 y2 = 11 x = 2, y= 3, x = 6 y = 1141. 2x y = 1 ; 9x2 2y2 + 9 = 0 x = 1, y = 3 , x =7,y = 15

42. x + 2y = 2 ;

x = 1,y = ½ x= 2/5 y = 4/543. 4x + 2y = x2 + xy 4x = 2 x = 1, y = 3 x = 2 y = 544. Solve the following simultaneous equations and give your answers correct to four

decimal places. 2x + 3y + 1 = 0 ; x2 + 6xy + 6 = 0

x =1.1196, y = 1.0797 , x = 1.7863 y = 0.857545. Solve the equations 4x + y + 8 = x2 + x – y = 2 . x = 1 , y =2 , x = 4 , y = 10

46. Solve the simultaneous equations

and x + 6y = 3. x = 0, y = ½ , x = 15 , y = – 2 47. Given the curve y2 = 8(1 – x) and the straight

line = 4. Without plotting a graph,

calculate the intersection points for both graphs .

( ) and (– 1, – 4)

48. Solve the simultaneous equations 2x + 3y = 9

and .

x = 3 , y = 1 , x = 18 , y = – 9


and .

x = 9 , y = 12 ,x = – 6 , y = 2

50. Solve the simultaneous equations 3x – 5 = 2y and y(x + y) = x(x + y) 5

x = 3 , y = 251 . Given that M = 2x – y , N = 3x + 1 and R = xy – 8 . Find the values of x and y

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such that 2M = N = R .

x = – 2 , y = ; x = 9 , y = 4

52. Solve the simultaneous equations below and give

your answers correct to two decimal places,

x – 4y = 9 ; 3y2 = 7 .

x = 11.56 , x = 3.76 ; y = 0.64 , y = – 1.31

53. Solve the simultaneous equations 4x + y = 8 and x2 + x – y = 2 . x = – 2 , y = 0 , x = – 3 y = 4

Simultaneous Equations_09 SE_09

54. y = 2x + 8 ; 8x + y2 = 0

x= – 2 , y = 4 ; x = – 8 , y = – 8

55. y + x = 11 ; xy = 28

x = 4 , y = 7 , x = 7 , y = 4

56. y = 12 – x ; x2 + y2 = 90

x = 3 , y = 9 , x = 9 ,y = 3

57. y + 2x – 6 = 0 ; xy + y2 – 8 = 0

x = 2 , y = 2 ; x = 7 , y = – 8

58. 2x + 3y = 8 ; 2x2 + 3y2 = 110

x = 7 , y = – 2 ; x = – 19/5 ‘ y = 26/5

59. 5y – 6x = 2 ; 4y2 – 3x2 – 4xy = 0 x = 4/3 , y = 2 ; x = – 4/17 , y = 2/17

60. 2x – 5y = 12x2 – 5y2 = 7

x = 1 , y = – 1 ; x = – 3/2 ‘ y =– 2

61. x + 3y = 3 ;

x = 1 , y = 2/3 ; x = 3/2 , y = ½


62. x + y = 9 ; xy = 8

x = 1 , y = 8 ; x = 8 , y = 1

63. x + y = 4 ; x2 + y2 – 76 = 3xy

x = – 2 , y = 6 x = 6 , y = – 2

64. x – y = 2 ; y – 1 =

x = – 2 , y = – 4 , x = 5 , y = 3

65. 2 p + q = 5 ; p2 + q2 = 10

p = 3 , q = – 1 , p = 1 , q = 3

66. 3p – q = 7 ; p2 + pq – q2 = 1

p = 5 , q = 8 ; p = 2 , q = – 1

67. 2x + 3 y = 10 ;

x = 4 , y = 2/3 ; x = ½ y = 3

68. 2x + 3y = 6 ; ( 2x +1 )2 + 6 ( y – 2 )2 = 49 x = – 3 , y = 4 ; x = 12/5 , y = 2/5

69. 2x + 4y = 9 ; 4 (x2+4y2) = 4 (5x+y) – 19 x = 7/2 , y = ½ ; x = 13/4 y = 5/8


70. 3m + 4n = 2 ; m2 – 1 = 3n2 m = 2 , n = – 1 , m = 14/11 , n = – 5/11

71. 2x – 3y = 6 ;

x = 1 , y = – 4/3 ; x = 6 , y = 2

72. h – k = 3 ; h2 + 3k = 10 . ( 4 sig. Figures)

h = 3.110 , y = 0.1100 ; h = – 6.110 , k = –9.110

73. m + n = 2 ; ( 3 dec.places)

m = 0.377,n =1.623 ; m = 1.178, n = 0.822

74. x + 2y = – 3 ; 7x + 3xy = 1

x = 2/3 , y = –11/6 ; x = 1 , y = – 2

75. 2x + 3y = 6 ;

x = – 3 , y = 4

76. x – 7y = 2 ; x2 – 7xy – 34 y2 = – 16

x = – 36/ 17 , y = – 10/17, x = 9 , y = 1

77. 3x + y – 4 = x2 – y + x = 4

x = 2 , y = 2 ; x = – 6 , y = 26


78. x + 3y = – 7 ; y2 – 2x + y = 8

x= – 4 , y = – 1 ; x = 11 , y = – 6

79. p – m = 7 ; p2 + 3m = 12 ( dec. places )

p = 4.437, m = – 2.563 ; p = – 7. 437 , m = – 14.437

80. ; y2 + 3 = 5x

x = 19/5 , y = – 4 ; x = 12/5 , y = 3

81. 2x + y = 1 ; 2x2 + 3xy + 4 = 0 ( 3 dec. places)

x = 1.443 , y = – 1.886 ; x = – 0.693, y = 2.386

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82. 3x – 2y = 6 ; 2x2 + 4xy – 2 = 0

x = 1.651 , y = – 0.524 ; x = – 0.151 y = – 3.227

83. 2x + 5 + y = 7 ; y ( x + y ) – x (y + x ) = 20

x = – 4/3 , y = 14/3 , x = 4 , y = – 6

84. x – 2y = 1 ;

x = 3 , y = 1 , x = – 3/5 , y = – 4/5

Name : _____________________________________

Form : _____________________________________Simultaneous Equations_13 SE_13


x – 2y = 1 ;

[ x= 3 , y =1 , x= – 3/5 , y = – 4/5 ]

86. Solve the simultaneous equations 2x – 3y + 4 = 0 ; x2 – 5xy – 1 = 0

Give your answer correct to 4 significant figures. [ x = –2.698, y = – 0.4655 ; x = – 0.1595 , y = 1.227 ]

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87. Solve the simultaneous equations.

[ x = – 9.216 , y = – 3.108 ; x = 0.216 y = 1.608 ]

88.Given that (– 2p, 3k ) is a solution to simultaneous

equation x + 2y =3 and x2 + y2 = 5 . find the value of p and k. [ p=1/2 , k=2/3 , p= – 11/10 , k = 2/15 ]

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Latihan Simultaneous Equation