Given the widespread dissemination of misinformation on social media, implementing fact-checking mechanisms for online claims is essential. Manually verifying every claim is very challenging, underscoring the need for an automated fact-checking system. This paper presents our system designed to address this issue. We utilize the Averitec dataset (Schlichtkrull et al., 2023) to assess the performance of our fact-checking system. In addition to veracity prediction, our system provides supporting evidence, which is extracted from the dataset. We develop a Retrieve and Generate (RAG) pipeline to extract relevant evidence sentences from a knowledge base, which are then inputted along with the claim into a large language model (LLM) for classification. We also evaluate the few-shot In-Context Learning (ICL) capabilities of multiple LLMs. Our system achieves an ‘Averitec’ score of 0.33, which is a 22% absolute improvement over the baseline. Our Code is publicly available on https://github.com/ronit-singhal/evidence-backed-fact-checking-using-rag-and-few-shot-in-context-learning-with-llms.