Final answer:
President Johnson established Medicare to provide healthcare insurance for the elderly and the Economic Opportunity Act of 1964 to fight poverty, both part of his Great Society initiative aimed at promoting social good.
Step-by-step explanation:
Two significant social programs established by President Lyndon B. Johnson as part of his Great Society initiative were Medicare and the Economic Opportunity Act of 1964. The purpose of Medicare was to provide a national insurance program for the elderly, ensuring they had access to healthcare regardless of their individual financial situation. The Economic Opportunity Act aimed at ending poverty through various measures including the Job Corps, which provided vocational training and employment opportunities for young people, and the Neighborhood Youth Corps, offering work-study programs for poor high school students. These programs exemplify Johnson's efforts to use government resources to reduce suffering and promote social good.