<![CDATA[This study aims to generate descriptions about mathematical representation of the students of Class IX SMP Alkarim of Bengkulu City using Two-Variable Linear Equation System (TVLES) based on extended level triad ++ after exploratory study. The test instrument is about to find out by exploring (exploratory study) students mathematical representation about set operations based on the Extended level Triad ++. The steps taken in the development of test instruments were such as, the preparation of the research permit, the implementation of the test, correcting and analyzing the test results, grouping the students into the levels of the Extended Level Triad ++ based on the test results, selecting subjects which were two students from each level to be interviewed, conducting trial interviews with several Class IX students, revising interview guidelines, conducting interviews with selected subjects using interview guides and audio recordings, analyzing data, making recapitulation of data and conclusion, and finally preparing reports. The subjects of this research were the students of Class IX of SMP Alkarim of Bengkulu City academic year 2015/2016 with total of 11 students. Based on the result of the research and discussion, it was generated the descriptions of mathematical representation of the students of Class IX SMP Alkarim of Bengkulu City about Two-Variable Linear Equation System (TVLES) based on the extended level triad ++ after the exploratory study, which are the following: there was no student in Pre-Level 0 (Pre-Intra); there were 2 students for Intra Level (Level 0) i.e. AR and LR; there were 2 students for semi intra level (level 1) i.e. PS and NN; there were 2 students for Inter Level (Level 2) i.e. PR and RO; there were 3 students for Semi-trans level (level 3) i.e. QN, RA and SW; there was 1 student for level Trans (Level 4) which is MD; and for the extended trans level (Level 5) there was only 1 student i.e. HN. Keywords: Exploratory study, Mathematical Representation, Extended level Triad ++]]>
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