Any widow or widower of any honorably discharged veteran who meets the qualifications specified in Section 2.01 and who was a resident of the State of Illinois for a continuous period of one year immediately before making application, who has no adequate means of support, and is unable to earn a living is entitled to admission to the Illinois Veterans Homes at Anna and Quincy should vacant beds exist. Preference for filling vacant beds or for filling vacant beds from a waiting list shall be granted first to eligible veterans.