That is an utterly silly request. What's left, Astrology?
Easiest determination, in my view 3(-2) - 6(1) = -6 - 6 = -12 this is not zero (0). There is a unique solution. However, addition and subtraction seem awfully "algebraic" to me.
3x + y would be half of 6x-2y except for the operator. You are left with 6x=4 and 6x=3. Again, this does use algebraic concepts, but I just did it without the equations.