Thanks, that makes more sense now.
I might have eventually realized that my system was cancelling out because it was using mutually derived equations, but I probably never would have realized that I was treating I_{3} as if it were flowing in two directions at once.
Using two of the...
Homework Statement
Homework Equations
Kirchhoff's loop rule and (maybe) Kirchhoff's current law
The Attempt at a Solution
So I attempted to apply Kirchhoff's loop rule to the circuit, and ended up with a system of linear equations:
24 - 6I_{1} - 3I_{3} = 0 \rightarrow...