Solve a System of Linear Equations
APL, 1 char

I know it doesn't fit the (revised) requirements, but it's too good not to post:

⌹


Symbol "domino" ⌹ (division ÷ inside a rectangle) performs matrix division, therefore it can solve any system of linear equations. You just have to put it between the constant term vector and the matrix with the other terms:

      8 ¯11 ¯3 ⌹ ⊃(2 1 ¯1)(¯3 ¯1 2)(¯2 1 2)
2 3 ¯1


(if you want to try it on TryApl, ⊃ is ↑)