Statics - Confusion about forces direction

[Femme_physics]

This is NOT a homework question. Just trying to understand a basic concept about signs convention...
[PLAIN]http://img638.imageshack.us/img638/9334/spring62009.jpg

Support A and B allow rotation, but nothing else.

Now, if I know W = 400 [N] for instance, using sum of all moments on B and sum of all forces on X I can find Bx = 920 and Ax = 920. It's easy for me to know which sign to use since there's only 1 force in each equation.

Here comes the kicker, though. I need to find Ay and By. I got two equations and two unknowns.
Sum of all moments on W, and sum of all forces on Y axis.
But, if I write Ay and By with the same signs (both plus or both minuses) they'd end up a different result if they had different signs (one plus the other a minus). My lecturer always told us that the sign of the result will let us know whether the original sign we picked was correct. But, when I have two equations and two unknowns, if I get a sign wrong it makes a different result!

So, am I suppose to intuitively know Ay and By are opposite signs because of some mechanically principle of rotation, or is there a way to mathmatically verify it through the equations?

 

[AlephZero]

It doesn't matter what direction you choose. If you "guess" the wrong direction, the magnitude of the force willl come out as a negative number.

In complicated problems it is often easiest just to say that all forces as positive in the positive X and positive Y directions, and let the algebra sort out the minus signs for you.

Work through the question making different assumptions and you will see how the equations change when you sum the forces and moments, and how the answers change when you solve the equations.

 

[Femme_physics]

Sorry it took me A WHILE to reply. I was meaning to get back to that. It's just that I'm still confused.

Yes, I do understand the idea that minus and plus are about direction. But reviewing my question, I made a mistake, and as it turns out, the terms cancel each other out and I get 0 = 0!

I want to rephrase the question so I'm making another topic in HW section, because I want to go over this specific question and this specific equations. Thanks though.

https://www.physicsforums.com/showthread.php?p=3249340#post3249340