Hazrat Asim and Hazrat Hammad both state, respectively, that Hazrat Ibn Sirin and Ibrahim, both of them, said: When you say, "Hayyak Allah" (May Allah give you life), then you should also offer Salam (greeting of peace) along with it.

27430 - (W) (1) From Abu Ma'shar, from Ibrahim.

27431 - From Hammad, from Ibrahim (they both said): If you say: "Hayyak Allah" (May Allah give you life), then reply: "With peace."

Hazrat Abdul Hameed says that Hasan Basri considered it disliked to say: Hayyak Allah, unless he also said Salam.

Hazrat Muhammad bin Sawqah narrates: Hazrat Maymun bin Mehran came to us, so a man said to him: "Hayyak Allah" (May Allah keep you alive). He replied: Do not say it like this. This is the greeting of the youth. Rather, say: "Hayyakum Allahu bis-salam." (May Allah keep you alive with peace.)

Hazrat A’mash says that Ibrahim stated: The Companions liked that when a person said to another,“Hayyak Allah (May Allah give you life),”he should also say Salam along with it.