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Two lines L1: 2y - 3x - 6 = 0 and L2: 3y+x-20 = 0 intersect at point A.

  1. Find the coordinates of A.
  2. A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y = mx +c, where m and c are constants.
  3. Another L4 is parallel to L1 and passes through (-1, 3). Find the x and y intercepts of L4

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  1. 2y – 3x = 6
    3y + x = 20
    2y - 3x = 6
    9y + 3x = 60
    11y = 60
    Y= 6
    X = 20 -18
    = 2
    Co-ordinates of A are (2,6)
     
  2.  L2: 3y = -x + 20
    y = - 1/3 x + 20 
    Gradient of perpendicular = 3
    (y-6)/(x-2) =3
    Y= 3X- 6 + 6
    Y = 3X
     
  3. Gradient of L4= gradient of L1
    =3/2
    (y-3)/(x-1) 3/4
    2y -6 = 3X + 3
    2y - 3X = 9
    When X = 0 y = 4.5
    When y = 0 x = -3

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