What government act in 1935 initiated the development of the federal-state unemployment insurance system?

The Social Security Act, enacted in 1935, is the correct answer as it established the framework for the federal-state unemployment insurance system. This act was part of a broader package of social welfare programs designed to provide a safety net for individuals during times of unemployment, old age, and disability. It allowed states to create their own unemployment insurance programs while receiving federal funding to help support those programs.

The significance of this act lies in its recognition of the need for a system that could provide temporary financial assistance to the unemployed, thereby promoting economic stability during the Great Depression. While other acts listed, such as the Fair Labor Standards Act and the National Labor Relations Act, focused on labor rights and standards, they did not address unemployment insurance directly. The Unemployment Compensation Act is often associated with the Social Security Act but is actually part of the broader framework set up under it. Thus, the Social Security Act stands out as the cornerstone legislation initiating the unemployment insurance system.