Mesh current method in finding currents
Take a look at the example circuit from here

from here: http://en.wikipedia.org/wiki/File:Mesh_Analysis_Example2_TeX.svg

Now take a look at the formulas for all 3 meshes:


If you ignore mesh 1, i.e. \$I_1 = 0\$ this circuit is similar to yours. You can see if the element that's part of both meshes shows up in both equations.