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  • SBS7484P
    SBS7484P's Avatar
    5,131 posts since Dec '07
    • 19 Jun `08, 10:12AM

      okay ive got a few questions regarding a maths simultaneous equations

      hope u guys can help

      question 1:

      Find the coordinates of each of the points of intersection of the curve xy=10 and the line 2x + 3y = 16

      Edited by SBS7484P 19 Jun `08, 10:15AM
  • SBS7484P
    SBS7484P's Avatar
    5,131 posts since Dec '07
    • 19 Jun `08, 10:14AM

      question 2:

      Find the coordinates of the points of intersection of the line x + y = 12 and the curve y = 10/x + x

  • jayh272416
    jayh272416's Avatar
    1,930 posts since Aug '07
    • 19 Jun `08, 10:16AM

      let me help you.

      x = 10/y -------- (1)
      2x + 3y = 16 --------- (2)

      sub (1) into (2)

      2(10/y)+3y = 16 ----- (3)

      Multiply each side of (3) by y

      20 + 3y^2 = 16y
      3y^2-16y+20 = 0 ------- (4)

      Factorise (4)

      (3y-10)(y-2) = 0
      y = 3 1/3 or 2
      When y = 3 1/3

      x = 10/ (3 1/3) = 3

      When y = 2

      x = 10/2 = 5

      Therefore the coordinates are:
      (5, 2) and (3, 3 1/3) 

  • SBS7484P
    SBS7484P's Avatar
    5,131 posts since Dec '07
    • 19 Jun `08, 10:17AM
      Originally posted by jayh272416:

      let me help you.

      x = 10/y -------- (1)
      2x + 3y = 16 --------- (2)

      sub (1) into (2)

      2(10/y)+3y = 16 ----- (3)

      Multiply each side of (3) by y

      20 + 3y^2 = 16y
      3y^2-16y+20 = 0 ------- (4)

      Factorise (4)

      (3y-10)(y-2) = 0
      y = 3 1/3 or 2
      When y = 3 1/3

      x = 10/ (3 1/3) = 3

      When y = 2

      x = 10/2 = 5

      Therefore the coordinates are:
      (5, 2) and (3, 3 1/3) 


      and this is for question 1 right?

  • jayh272416
    jayh272416's Avatar
    1,930 posts since Aug '07
    • 19 Jun `08, 10:19AM

      qn 2

      x+y = 12 ----- (1)
      y = 10/x + x ----- (2)

      Sub (2) into (1)

      2x + 10/x = 12 ----- (3)

      Multiply each side of (3) by x

      2x^2 + 10 = 12x
      2x^2 - 12x + 10 = 0
      x^2 - 6x + 5 = 0
      (x-5)(x-1) = 0
      x = 5 or 1

      If x = 5,
      y = 12-5 = 7

      If x = 1,
      y = 12-1 = 11

      Coordinates are:

      (5,7) and (1,11)

  • jayh272416
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    1,930 posts since Aug '07
  • SBS7484P
    SBS7484P's Avatar
    5,131 posts since Dec '07
  • SBS7484P
    SBS7484P's Avatar
    5,131 posts since Dec '07
    • 19 Jun `08, 10:32AM

      Find the coordinates of the points of intersection of the line 2x-y=5 and the curve x^2+xy=2

  • jayh272416
    jayh272416's Avatar
    1,930 posts since Aug '07
    • 19 Jun `08, 10:37AM
      Originally posted by SBS7484P:

      Find the coordinates of the points of intersection of the line 2x-y=5 and the curve x^2+xy=2


      2x-y=5------(1)
      x^2+xy=2-----(2)

      From (1)

      y = 2x-5 ----- (3)

      Sub (3) into (2)

      x^2 + x(2x-5) = 2
      3x^2-5x-2=0
      (3x+1)(x-2)=0
      x = -1/3 or 2

      when x = -1/3,
      y = -5 2/3

      when x = 2,
      y = -1

      coordinates are:

      (-1/3, -5 2/3) and (2,-1)

  • SBS7484P
    SBS7484P's Avatar
    5,131 posts since Dec '07
    • 19 Jun `08, 10:40AM

      thanks alot. =)

      another 25 questions of random coming up.. ah wait. i go make anotehr thred on that.. this title dun seem very app;ropriate

       

      mod pls lock thanks

  • fairlady_xoxo
    the stifmeister
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    11,316 posts since Jan '07
  • Gosu.
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    493 posts since Jul '06
  • honeymouse
    Possum is cute & delicious too!
    honeymouse's Avatar
    5,656 posts since Sep '06
    • 19 Jun `08, 10:57AM
      Originally posted by SBS7484P:

      Find the coordinates of the points of intersection of the line 2x-y=5 and the curve x^2+xy=2

      2x - y - 5 = 0 ------------ (Equation 1)

      x^2 + xy - 2 = 0 ----------- (Equation 2)

      Multiply (Equation 1 ) by x and hence:

      2x^2 - xy - 5x = 0 ............. (Let's call it Equation 3)

      Add Equation 3 to Equation 1:

      (2x^2 + x^2) + (-xy + xy) - 5x - 2 = 0

      --------> 3x^2 - 5x -2 = 0

      Now you should be able to factorise it.  It should have 2 coordinates (x1, y1) and (x2, y2).

       

       

  • CreativeMaggot
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    82 posts since Jan '08
  • MrSean
    MrSean's Avatar
    163 posts since May '08
    • 20 Jun `08, 3:52AM
      Originally posted by SBS7484P:

      okay ive got a few questions regarding a maths simultaneous equations

      hope u guys can help

      question 1:

      Find the coordinates of each of the points of intersection of the curve xy=10 and the line 2x + 3y = 16


      xy=10

      x=10/y -- (1)

      2x + 3y = 16 --(2)

      Sub (1) into (2): 20/y + 3y = 16

      20 + 3y^2 =16y

      3y^2-16y+20 = 0

      (3y-2)(y-10) = 0

      y = 2/3 OR y=10

      Sub y=2/3 and y=10 into (2)

      2x + 2 = 16     OR      2x + 30 = 16

      x = 7                            x = -7

      Therefore the coordinates are (7, 2/3) and (-7, 10).

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