Kirchoff's Law Problem
You have four relatively obvious current loops that could use KVL. That's all you need for mesh analysis. (You don't need to include any KCL statements for the nodes.)







simulate this circuit &ndash; Schematic created using CircuitLab

I've labeled each clockwise-going current loop inside each independent loop, which hopefully will be obvious to you. The following equations will make it explicit and if the above loops aren't obvious from the schematic then they will be from the equations below. I will start each loop from their lower-left corner position and I will follow around that loop in clockwise (with the current) direction:

$$\begin{align*}
0\:\text{V}-I_1\cdot R_6-\left(I_1-I_2\right)\cdot R_3-\left(I_1-I_4\right)\cdot R_1&amp;= 0\:\text{V}\\\\
0\:\text{V}+V_3-\left(I_2-I_4\right)\cdot R_2-\left(I_2-I_1\right)\cdot R_3-V_2-\left(I_2-I_3\right)\cdot R_5 &amp;= 0\:\text{V}\\\\
0\:\text{V}-\left(I_3-I_4\right)\cdot R_4-\left(I_3-I_2\right)\cdot R_5-I_3\cdot R_7&amp;= 0\:\text{V}\\\\
0\:\text{V}+V_1-\left(I_4-I_1\right)\cdot R_1-\left(I_4-I_2\right)\cdot R_2-V_3-\left(I_4-I_3\right)\cdot R_4 &amp;= 0\:\text{V}
\end{align*}$$

From the above, you should be able to solve for all of \$I_1\$, \$I_2\$, \$I_3\$, and \$I_4\$. With those in hand, node voltages (if you set a ground point on one of the nodes, anyway) and the net currents in devices can all be readily computed.