Using Nodal Analysis to determine current in a resistor

[TheBigDig]

Homework Statement

Homework Equations

$V = IR$
$\sum_{k = 0}^{n} I_k = 0$

The Attempt at a Solution

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I set the bottom node as the reference node and worked from there to find the three equations for the loop. When I try to eliminate $I_4$ by using $I_4 = I_2 - I_3$ I run into a problem were both $I_2$ and $I_3$ scale equally are both eliminated from the simultaneous equation. I tried manipulating $I_1$ to solve it but got the wrong answer. Any help would be appreciated as I am new to nodal analysis.

 

[gneill]

You're doing loop analysis (KVL) but they want you to use nodal or source transforms.

Can you write node equations using the given component values? The only variables you should introduce are the node potentials. No current variables!