The sign of the current flowing in a circuit I was doing the following problem: 

And I was asked to find Iy.
I found Iy to be 2.64 using KCL. However, the right answer was negative 2.64. 
Is it negative only because there is a dependant voltage source with "+ -" ? And why must it be negative? Does "-" in the final answer play a significant role? If I put positive 2.64 instead of negative, would that be wrong?
Also, here is another question 

I found V1 to be 11.9. However, the right answer was - 11.9.
Can someone clarify for me when do you put negative sign?
 A: When you are given the problem, you can safely make assumptions about the direction of currents. When you solve the problem using Kirchhoff's laws, ending up with a negative current is absolutely fine. The negative sign in the current is just an indication that your initial assumption about the direction of the currents were wrong. If you get the answer to be a negative number, then just flip the direction of the current in the corresponding branch. You needn't solve the problem again, even if you did you will end up with the same answer.
In your first question, the question has already mentioned the direction of the current iy. The answer turns out to be negative because, the current isn't in the direction as mentioned in the question. The current is in the opposite direction. 
The same goes for the second question.
A: To solve circuit problems all you need to do is choose a convention and then apply KVL and KCL.  
When labelling the circuit the choice of current directions and voltages is arbitrary and if you find that after all the algebra a current comes out to be negative than all that means is that the initial current direction chosen when labelling was wrong and the current actually flows in the opposite direction.

KCL 

Label the nodes making one of them the zero volt node. 
KCL is derived from the law of conservation of charge and requires the algebraic sum of the currents entering (or leaving) a node to be zero. 
Choosing to sum the currents leaving node $nV_x$ you get 
$\dfrac {nv_x - V_1}{R_1} + \dfrac {nv_x - 0}{R_2} + i_y = 0$
Notice that since the currents leaving the junction are being found the voltage across any resistor is the voltage at the node minus the voltage at the other end of the resistor ($V_{\text{node}} - V_{\text {other end}}$).
For currents entering the node the voltage across any resistor would be the voltage remote from the node minus the node voltage.  ($V_{\text{other end}} - V_{\text {node}}$)
So the equation for currents entering the node would be
$\dfrac {V_1 - nv_x}{R_1} + \dfrac {0- nv_x}{R_2} - i_y = 0$
The same equation as before.

KVL 
A convention which is often used to label circuit diagram prior to using KVL is called the associated variables convention.  
Label a current direction for every circuit component and then the voltage label with a plus sign where the current enters the component.
Instead the voltage can be labelled and the current then labelled going in to the circuit element at the plus sign end.  

KVL is derived from the law of conservation of energy.
When going round a loop assign a sign to the voltage which is the sign at the end where you are entering the circuit element and the sum of these voltages should be zero.  
Starting at the bottom left hand corner and going clockwise gives 
$-V_1 =i_xR_1+nv_x = 0$
You now have two equations and two unknowns $v_x$ and $i_y$ which give $v_x = 13.2$ V and $i_y = -2.64$ A.  
The current direction was guessed incorrectly by the setter of the problem.
So the analysis of the circuit has yielded this:

A: In first Question, $V_x$ is 13.2V and the current flowing in R1 is +4.4A. And the current flowing in R2 is +7.04A(=13.2*4/7.5). Using KCL, Iy must be -2.64A. The sum of currents flowing into that node is equal to the sum of currents flowing out of that node. In the circuit 4.4A is flowing into top node from R1 and 7.04A is flowing out of the node to R2. So 2.64A must flow into the node and the sign of $I_y$ must be minus.
Remember polarity of voltage or current matters a lot and be careful.
A: Kirchoff's current law (KCL) states that "The algebraic sum of all currents entering and exiting a node must equal zero". By algebraic care must be taken to choose a convention whereby you set currents flowing into the node as positive (+ve) and subsequently those flowing out of the node as negative (-ve) or vice versa. This should sort you out. Use this reference too.
