As the complexity of Software Engineering (SE) tasks continues to escalate, Multi-Agent Systems (MASs) have emerged as a focal point of research and practice due to their autonomy and scalability. Furthermore, through leveraging the reasoning and planning capabilities of Large Language Models (LLMs), the application of LLM-based MASs in the field of SE is garnering increasing attention. However, there is no dedicated study that systematically explores the design of LLM-based MASs, including the Quality Attributes (QAs) on which designers mainly focus, the design patterns used by designers, and the rationale guiding the design of LLM-based MASs for SE tasks. To this end, we conducted a study to identify the QAs that LLM-based MASs for SE tasks focus on, the design patterns used in the MASs, and the design rationale for the MASs. We collected 94 papers on LLM-based MASs for SE tasks as the source. Our study shows that: (1) Code Generation is the most common SE task solved by LLM-based MASs among ten identified SE tasks, (2) Functional Suitability is the QA on which designers of LLM-based MASs pay the most attention, (3) Role-Based Cooperation is the design pattern most frequently employed among 16 patterns used to construct LLM-based MASs, and (4) Improving the Quality of Generated Code is the most common rationale behind the design of LLM-based MASs. Based on the study results, we presented the implications for the design of LLM-based MASs to support SE tasks.