Application of Kirchoff's Laws to circuit with multiple loops
Nothing in the diagram indicates that the low sides of batteries are tied to the same potential.  You should ask your professor whether or not you can assume that they are.

I suspect that this is a trick question, so I'll assume that the batteries are not tied to the same rail.  

Intuition without Kirchhoff. The first thing that catches attention is that these are 2 separate sub-circuits that are connected at only one point with the 20Ω resistor.  If I assume that there is current through 20Ω, then it would have to have a return path.  That is, another connection between the 2 sub-circuits.  But there isn't another connection.  So, there should be no current through 20Ω, which makes the problem a lot simpler.

Now add Kirchhoff.  How to back-up the intuition with formal Kirchhoff?  You wanted to replace the open circuit (&infin; Ω) at the bottom of the schematic with a wire (0 Ω) in order to get enough equations.  Going from &infin; to 0 just like that... doesn't sound quite right.  Instead, draw a resistor with infinite resistance there.
Include this resistance into your new equation.  Of course, you'll have I = V/R = V/&infin;  = 0 in some equations, and that's the same as saying that no current flows through an open circuit.

So there.  @Groki, you do the algebra.