Epilepsy is the most common neurological disease defined as a central nervous system disorder that is characterized by recurrent seizures. While electroencephalography (EEG) is an essential tool for monitoring epilepsy patients' brain activity and diagnosing epilepsy, Visual detection of the EEG signal to identify epileptic seizures is a time-consuming approach that might result in human error. Therefore, an early and precise epilepsy diagnosis is critical to reducing the risk of future seizures. This paper aims to increase epileptic seizure detection accuracy in a balanced dataset while reducing the execution time. To address this, we proposed a hybrid system of supervised and unsupervised machine learning algorithms to construct a computationally efficient and scalable model for the early detection of epileptic seizures from two-class EEG datasets. First, Discrete Wavelet Transform (DWT) was applied to the EEG signal to decompose it into frequency sub-bands. Then these EEG extracted features were fed into the Gaussian Mixture Model (GMM) for partitioning these features into two clusters: epilepsy or not. Lastly, the clusters' output was evaluated with the random forest classifier. In addition, Principal Component Analysis (PCA) was used to reduce the EEG features and to reduce further the features obtained after conducting DWT on the EEG signal to determine the impacts of dimension reduction on this system performance. The experimental results show that the highest accuracy was achieved by the hybrid system of GMM with random forest with DWT features with an accuracy of 93.62 %.