This research was conducted in response to the learning obstacles identified in teaching the system of linear equations with three variables, based on the preliminary study results at SMK Negeri 1 Padaherang. This study utilized a qualitative approach with Didactical Design Research design. Findings from the study indicated that students still faced difficulties in understanding concepts, prerequisite materials, constructing mathematical models, and employing elimination and substitution methods within the subject matter. To address these issues, the researcher developed a learning trajectory with the aim of enhancing the quality of instruction. Identification of learning obstacles served as the basis for designing a Hypothetical Learning Trajectory (HLT) for the system of linear equations with three variables at the vocational school.
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