This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms, students face such a situation when they learn the classic methods to solve systems involving 2 linear equations with 2 unknowns. Results from this empirical study show that extending previous algebraic syntax to the 2nd tier of representation of the unknown requires fundamental reconceptualizations such as that of algebraic equalization and that of mathematical unknown. (Contains 10 tables and 8 footnotes.)