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**1. Homework Statement**

**2. Homework Equations**

Kirchhoff's loop rule and (maybe) Kirchhoff's current law

**3. 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[itex]_{1}[/itex] - 3I[itex]_{3}[/itex] = 0 [itex]\rightarrow[/itex] 2I[itex]_{1}[/itex] - I[itex]_{3}[/itex] = 8

36 - 6I[itex]_{1}[/itex] - 6I[itex]_{2}[/itex] = 0 [itex]\rightarrow[/itex] I[itex]_{1}[/itex] + I[itex]_{2}[/itex] = 6

12 - 3I[itex]_{3}[/itex] - 6I[itex]_{2}[/itex] = 0 [itex]\rightarrow[/itex] 2I[itex]_{2}[/itex] + I[itex]_{3}[/itex] = 4

but every time I try to solve it, I end up with everything dropping out. I'm not sure what I'm missing here, but I've been banging my head against this one for about 4 hours now, so any help would be appreciated!

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