Question
Sat September 01, 2012 By:
 

if lines ax+12y+1=0 , bx+13y+1=0 , cx+14y+1=0 are concurrent then a,b,c are in which series (show working)

Expert Reply
Sun September 02, 2012

Equation of three lines L1, L2 and L3 are:

L1: ax + 12y + 1 = 0                … (1)

L2: bx + 13y + 1= 0                 … (2)

L3:  cx + 14y + 1 = 0               … (3)

 

Since, these three lines are concurrent so, they must intersect at a point.

To find the point of intersection of the lines, it is required to solve at least any two equations, let say equations (1) and (2).

Multiplying 13 and 12 in both sides of equations (1) and (2) respectively and subtracting these results;

13(ax + 12y + 1) - 12 (bx + 13y + 1) = 0

13ax + 156y + 13 - 12bx - 156y - 12 = 0

(13a - 12b)x + 1 = 0

(13a - 12b)x = -1 

Substituting this value in equation (1);
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