Cyberbullying is a form of bullying that occurs through digital technology on various social media platforms. This issue has become critical, particularly when it involves racial statements that can threaten community harmony. Many researchers worldwide are working on solutions for automatic hate speech and cyberaggression detection using different machine learning models. This study aims to introduce a novel hybrid method for detecting cyberbullying, utilizing a combination of Support Vector Machine (SVM) and Linear Discriminant Analysis (LDA), collectively referred to as SVM-LDA. The methodology involves integrating SVM and LDA techniques. The models efficiency was assessed using various metrics, offering a comparative analysis of the hybrid model against individual machine learning models. The results show that the proposed hybrid model achieved 96.1% accuracy and outperformed single machine learning models on the Twitter dataset. The hybrid model also demonstrated robustness in handling imbalanced classes for cyberbullying detection. The proposed SVM-LDA hybrid approach shows significant potential in effectively detecting cyberbullying, even in cases of class imbalance. This model offers a more robust solution compared to traditional single machine learning models in detecting cyberaggression.