Question

For what value of K, are the three lines x -2y +1= 0; 2x -5y +3 = 0 and 5x -9y +K = 0 are concurrent? 

Answer 1

The given equation of straight lines are 

Straight lines (1), (2) and (3) will be concurrent if they pass through same point The point of intersection of (1) & (2) is given by 

or x=l,y=1 Le. P (1,1).

Lines (1), (2) and (3) will be concurrent if point P(I,I) of intersection of (1) and (2) would lie on (3) 5(1) -9 (1) + K = 0 

or K=4