The powers granted in sections 31-1008, 31-1009 and this section shall be deemed to be, and hereby are, extended and shall apply to sections 31-1005 to 31-1007, and 31-1101, whenever any county and such cities shall, jointly, at such election, have determined to acquire a site or sites and construct, equip and furnish such public buildings without the issuance of bonds therefor.