I'm not aware of a "system of equations palette", so I may be missing something, but I believe what is happening is that you are using a form from one of the palettes that is intended for styling and layout of stuff. By using it in an Input cell, Mathematica is expecting to be able to evaluate whatever you put there. I don't know what that left bracket thing is supposed to mean for evaluation, so I don't know specifically how to explain its use.
One thing I can point out is that you are using Set instead of Equal. If this thing really is supposed to solve a system of equations, then I suspect it expects Equal.
But if you really just want to solve a system of equations, you could use Solve:
Solve[{x + y == 1 && y == 2}, {x, y}]
(*{{x -> -1, y -> 2}}*)