Question

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

Answer 1

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