The correct option is B k = 2
The pair of linear equations, 13x+ky−k=0 and 39x+6y−(k+4)=0 has infinitely many solutions if:
a1a2=b1b2=c1c2
⇒1339=k6=−k−(k+4)
⇒13=k6=kk+4
Equating the 1st and 2nd part of the above equation we get,
13=k6
⇒k=2
OR
Equating the 1st and 3rd part of the above equation we get,
13=kk+4
⇒k+4=3k
⇒2k=4
⇒k=2
∴ When k = 2, the pair of linear equations has infinite solutions.