You might want to add some dates, or approximate dates, for those in your query.Without dates, I'm not sure if Adelia and Edgar died in a time period where they would have generated death certificates.TX began keeping vital records in 1903.
Without dates, I don't know if this is your Adelia. TX Dth Idx Online 1964-1998:
Anna Adelia Victoria Anderson, d 26 Jan 1994 Travis Co, TX.
Adelia A. Anderson, b 22 Dec 1898; d 26 Jan 1994; last residence Austin, Travis Co, TX; SS card issued in TX.
IL began keeping state vital records in 1916, but some counties began earlier.So, it might depend not only the date, but the county of their birth.
Since you know where Adelia and Edgar are buried, you probably have dates for them. Happy Hunting.