The correct option is A k = 9
Given: 2x+3y−5=0
6x+ky−15=0
Condition for infinitely many solutions is:
a1a2=b1b2=c1c2
a1=2, a2=6, b1=3, b2=k
26=3k⇒k=9
When k=9, it represents two exactly same lines, so all the points coincide, thus giving infinitely many solutions.