The correct option is C k=6
Give: x+2y=3
3x+ky−15=0
Condition for no solution:
a1a2=b1b2≠c1c2
a1=1, a2=3, b1=2, b2=k
13=2k≠315⇒k=6
When k=6 the set of equations represents two parallel lines which don't intersect at any point. So they can't have a common point which would be the solution.