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,

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.