Difficulties in learning linear algebra are well-documented and arise from epistemological, didactic, and instructional factors. This study presents the design of an affective intelligent tutor focused on the mathematical object known as systems of linear equations (SLE). The tutor provides adaptive feedback and was developed using an iterative methodology that combines design, internal validation, and continuous improvement. It integrates several components: A didactic knowledge module, a model of ideal student behavior, a pedagogical tutoring module, a graphical interface, and an affective module based on computer vision. This affective component employs the DeepFace library, integrated with OpenCV and PyQt6, to detect emotions in real time through facial expressions. Emotional inputs are processed to compute a stress index, which triggers adaptive, affective feedback during task execution. The current version includes one task designed to help students coordinate the seven different representations of a 3 × 2 SLE, thereby enhancing their understanding of the solution set. To date, expert and functional validation has been conducted. The tutor shows potential as a support tool for autonomous learning and as a training resource for future mathematics teachers. Preliminary testing with experts revealed challenges such as redundant emotion detection and visual overlap of interface elements. These findings have informed subsequent redesign efforts. Although still in the prototype phase, the system shows promise in supporting representational coordination in tasks involving SLE.