Speech Emotion Recognition (SER) is an evolving area of research within human-computer interaction, aiming to enable machines to detect and interpret emotional states conveyed through speech. This paper presents a hybrid SER system that leverages both Support Vector Machine (SVM) and Neural Networks to enhance the accuracy and adaptability of emotion classification. SVM, a supervised learning model, is employed for its effectiveness in high-dimensional spaces and robustness in handling smaller datasets, making it suitable for precise emotion classification based on extracted features such as pitch, energy, and Mel-frequency cepstral coefficients (MFCCs). Neural Networks, particularly deep learning architectures, are used for automatic feature extraction and modelling complex, non-linear patterns in the speech data. This hybrid approach enables the system to balance interpretability and performance, ensuring both efficiency and depth in learning emotional cues. The system supports multilingual inputs and provides personalized emotional feedback through an intuitive web interface developed using Streamlit and Flask. Experimental results demonstrate improved recognition accuracy, showcasing the potential of combining classical and deep learning techniques in real-world applications of emotion-aware systems.