Find the value of k such that the equations 2x+3y+11=0 and 6x+ky+33=0 represent coincident lines.

Correct option is C

Given:

Two equations:

2x + 3y + 11 =0

6x + k y+ 33=0

Concept Used:

For two lines to be coincident, their coefficients must be proportional:

​$$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$$​​

Solution:

​$$\frac{2}{6} = \frac{3}{k} = \frac{11}{33}$$​​

​$$\frac{1}{3} = \frac{1}{3} \quad \text{(True, so correct proportion)}$$​​

​$$\frac{3}{k} = \frac{1}{3}$$​​

k=9

Option (C) is right.