<p>Algebra has long been considered a challenging subject to teach and learn. Recently, large language models (LLMs) have garnered attention in education, but a comprehensive overview of their effectiveness in facilitating algebra education is still lacking. Guided by the C-AI-TPACK framework, this systematic review provides insights into the applications of LLMs to the algebra domain. Following the PRISMA framework, a search across six databases identified 1,338 records, with 49 refereed publications retained. Results showed that most reviewed studies employed LLMs (1) to analyze primary data sets; (2) mainly for learning; (3) frequently focusing on ChatGPT; (4) to automatically solve algebra problems; (5) to report both benefits and challenges related to algebra content and pedagogical knowledge using the C-AI-TPACK framework; (6) lacking a comprehensive consideration of their contextual factors; (7) equally using qualitative and quantitative evaluation methods to evaluate LLM performance; and (8) frequently applying the zero-shot prompting method. The reviewed studies also compared LLM performance across domains and models. Theoretically, this review highlights the benefits and challenges of using LLMs in the algebra domain through the lens of the C-AI-TPACK framework. Practically, it provides evidence-based guidance and suggestions for using LLMs effectively in the algebra domain.</p>