Simultaneous Linear and Non-Linear Equations in Two Unknowns

• Daisuke-kun

  8 Jan 08, 18:14

  nid help
  
  1) 3s^2 + 2t^2 =11
  3s + 2t = 1
  
  2) 3x - 2y = 1
  (x-2)^2 + (2y+3)^2 = 26
  
  3) 3y - x = 3
  2/3y - 1/x = 2
  
  4) find the coordinates of the points where the line 2x+5y+4=0 intersects the curve 2xy = -1
  
  5) The curve xy + 20 = 5x and the line 2y = x-3 intersects at points A and B.
  Calculate the coordinate of A and B
  
  Workings might help.
  so damn difficult.
  i can do other questions except tis...
• FireIce

  8 Jan 08, 18:22

  use substitution
• lpx88

  8 Jan 08, 18:29

  Originally posted by Daisuke-kun:

  nid help
  
  1) 3s^2 + 2t^2 =11
  3s + 2t = 1
  
  2) 3x - 2y = 1
  (x-2)^2 + (2y+3)^2 = 26
  
  3) 3y - x = 3
  2/3y - 1/x = 2
  
  4) find the coordinates of the points where the line 2x+5y+4=0 intersects the curve 2xy = -1
  
  5) The curve xy + 20 = 5x and the line 2y = x-3 intersects at points A and B.
  Calculate the coordinate of A and B
  
  Workings might help.
  so damn difficult.
  i can do other questions except tis...

  Qn 5 seems damn familiar. TYS qn ah Aiya all sub in la
• eagle

  8 Jan 08, 19:05

  Originally posted by Daisuke-kun:

  nid help
  
  1) 3s^2 + 2t^2 =11
  3s + 2t = 1
  
  2) 3x - 2y = 1
  (x-2)^2 + (2y+3)^2 = 26
  
  3) 3y - x = 3
  2/3y - 1/x = 2
  
  4) find the coordinates of the points where the line 2x+5y+4=0 intersects the curve 2xy = -1
  
  5) The curve xy + 20 = 5x and the line 2y = x-3 intersects at points A and B.
  Calculate the coordinate of A and B
  
  Workings might help.
  so damn difficult.
  i can do other questions except tis...

  I'm going out, so I shall do question 4 and 5 first. 1,2,3 use substitution, similar to what I am going to do for 4 and 5
  
  4)
  2xy = -1
  x = -1/2y
  
  2x + 5y + 4 = 0
  Sub x = -1/2y
  -1/y + 5y + 4 = 0
  5y^2 + 4y - 1 = 0
  (5y - 1) (y + 1) = 0
  y = 1/5 or y = -1
  x = -5/2 or -1/2
  
  5) 2y = x - 3
  
  xy + 20 = 5x
  2xy + 40 = 10x
  Sub 2y = x - 3
  x(x-3) + 40 = 10x
  x^2 -13x + 40 = 0
  (x-5) (x-8 ) = 0
  x = 5 or 8
  y = 1 or 2.5
  
• Daisuke-kun

  8 Jan 08, 19:35

  thx eagle.
  question 4.
  ur ans.
  the -1/2 is actually 1/2
  
  but i'm stuck with 1 & 3
  
• eagle

  8 Jan 08, 19:48

  Originally posted by Daisuke-kun:

  thx eagle.
  question 4.
  ur ans.
  the -1/2 is actually 1/2
  
  but i'm stuck with 1 & 3
  

  yup yup, typo...
• eagle

  8 Jan 08, 19:50

  Originally posted by Daisuke-kun:

  nid help
  
  1) 3s^2 + 2t^2 =11
  3s + 2t = 1
  
  2) 3x - 2y = 1
  (x-2)^2 + (2y+3)^2 = 26
  
  3) 3y - x = 3
  2/3y - 1/x = 2
  

  1)
  3s = 1 -2t
  
  3s^2 + 2t^2 = 11
  9s^2 + 6t^2 = 33
  Sub 3s = 1 -2t
  (1-2t)^2 + 6t^2 = 33
  Should be able to solve from here
  
  3)
  x = 3y - 3 => Use this in your substitution
  
  is 2/3y same as 2 / (3y) or is it (2/3) y?