I need to find the currents I1 and I2 in this circuit:

I apply KCL to node A to obtain:
5+1-I1-I2=0
or
I1+I2 = 6

However I am stuck here and cannot figure out how to solve this???

 

First look at the circuit and draw a closed loop path for the 1A current and 5A current. If you do that you will have the answer.

 

I need to find the currents I1 and I2 in this circuit:

I apply KCL to node A to obtain:
5+1-I1-I2=0
or
I1+I2 = 6

However I am stuck here and cannot figure out how to solve this???

As Jony130 said, just consider the obvious constraints. If 1A is flowing into the left of the 1A source, where does that current HAVE to be coming from? What does that say about I1?

If you want to proceed programmatically, you have done KCL at just one of the three nodes in the circuit. Do it at one of the other two to get a second equation. You can declare the third node to be any voltage you like (0V works good).