# If the lines 2x - 3y + k = 0, 3x - 4y - 13 = 0 and 8x - 11y - 33 = 0 are concurrent, then the value of k is

1.3k views

If the lines 2x - 3y + k = 0, 3x - 4y - 13 = 0 and 8x - 11y -  33 = 0 are concurrent, then the value of k is

(A)   7

(B)   6

(C)  -7

(D)  -6

+1 vote
by (53.8k points)
selected by

Correct option (c) (-7)

Explanation :

We have

Direct Method: Solving 3x -    4y  - 13 = 0 and 8x -    11y -33 =0, we obtain x = 11 and y = 5 so that (11, 5) is the intersection of these lines. The third line 2x - 3y + k = 0 also passes through (11, 5).

2(11) - 3(5) + k = 0

k = -7

+1 vote