How to find total voltage in a two loop circuit
&quot;How do I derive the value at I1?&quot;


Not sure what is the point of doing the substitution of a voltage supply \$V_2\$ by the current supply \$I_1\$, but to have both circuits having the same currents and node voltages you would need \$I_1\$ to be the current going into \$V_2\$


&quot;What is the correct value at I1 so I can check my work?&quot;


Using a simulator I got that \$I_1=-1.739 mA\$, so the power supply \$V_2\$ is outputting current, notice I am not referring to the current over resistor \$R_1\$ but to the value that would work if you did the substitution you mentioned (which I think is extra work and does not help solve the system).
To solve this using superposition, ignore that supply substitution and do this
To use superposition in this case you would solve the two single supply circuits and just add their currents.



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