voltage - A problem with branch current method

^{simulate this circuit – Schematic created using CircuitLab}

I'm trying to solve a cicuit with using the branch current method. Here is the circuit:

The words after the values are the unit in my language (Ом=Ohm), so both capacitors are 10 Ohms and so on. I have counted 2 nodes, I think the one is where the letter "b" is placed, and the other where "f" is placed. I made 1 equation using KCL, and three using KVL, but when I calculated the system of linear equations, the result was \$ 0=0 \$.

Equations: \$\$\begin{align} I_1+I_2-I_3-I_4&=0\quad \text{(from KCL for node 1)}\\ I_1*Z_1+I_3*Z_3&=E_1\quad \text{(KVL for circuit I)}\\ I_2*Z_2+I_4*Z_4&=E_2\quad \text{(KVL for circuit II)}\\ I_1*Z_1+I_4*Z_4&=E_1\quad \text{(KVL for circuit III)}\\ >\\ I_1+I_2-I_3-I_4&=0\\ -j10*I_1 + (10-10j)*I_3 &= 20\\ j20*I_2 + 10*I_4 &= 14,14 + j14,14\\ -j10*I_1 + 10*I_4 &= 20\\ \end{align}\$\$