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)

Asked by  | 1st Sep, 2012, 12:16: PM

Expert Answer:

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);

Answered by  | 2nd Sep, 2012, 12:13: PM

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