I studied 2x2 linear equation system in high school at 14 (13?) y.o. It was a technical school with more math and physics, and later specialization (like chemistry, electronics, building, ...). I think in a normal school they study that at 16 y.o.

We also teach 2x2 systems to 18 y.o. in the fists year of the university for architects, medics and other degree that don't need a huge amount on math. (Other degrees like engineering or physics get 4x4 or bigger systems that definitively need the Gauss method.)