Using Mathematica


Simplify [
      Solve [
              { 
                 V - I1 R1 - I3 R3 == 0 ,
                 I1 R1 - I2 R2 - I5 R5 == 0 ,
                 I3 R3 + I5 R5 - I4 R4 == 0 ,
                 I0 - I1 - I2 == 0 ,
                 I1 + I5 - I3 == 0 ,
                 I2 - I4 - I5 == 0 ,
                 Req == V / I0
               },
               {
                 Req, I0, I1, I2, I3, I4, I5
               }
             ]
         ]



Out[1]= {{Req ->

       R3 (R4 R5 + R2 (R4 + R5)) + R1 (R4 (R3 + R5) + R2 (R3 + R4 + R5))
>      -----------------------------------------------------------------,
             (R3 + R4) R5 + R1 (R3 + R4 + R5) + R2 (R3 + R4 + R5)

>     I4 ->

                         (R3 (R2 + R5) + R1 (R3 + R5)) V
>       -----------------------------------------------------------------,
        R3 (R4 R5 + R2 (R4 + R5)) + R1 (R4 (R3 + R5) + R2 (R3 + R4 + R5))

>     I2 ->

                          (R3 R5 + R1 (R3 + R4 + R5)) V
>       -----------------------------------------------------------------,
        R3 (R4 R5 + R2 (R4 + R5)) + R1 (R4 (R3 + R5) + R2 (R3 + R4 + R5))

>     I3 ->

                        (R1 R4 + R4 R5 + R2 (R4 + R5)) V
>       -----------------------------------------------------------------,
        R3 (R4 R5 + R2 (R4 + R5)) + R1 (R4 (R3 + R5) + R2 (R3 + R4 + R5))

>     I0 ->

            ((R3 + R4) R5 + R1 (R3 + R4 + R5) + R2 (R3 + R4 + R5)) V
>       -----------------------------------------------------------------,
        R3 (R4 R5 + R2 (R4 + R5)) + R1 (R4 (R3 + R5) + R2 (R3 + R4 + R5))

>     I1 ->

                          (R4 R5 + R2 (R3 + R4 + R5)) V
>       -----------------------------------------------------------------,
        R3 (R4 R5 + R2 (R4 + R5)) + R1 (R4 (R3 + R5) + R2 (R3 + R4 + R5))

                                  -(R2 R3 V) + R1 R4 V
>     I5 -> -----------------------------------------------------------------}
            R3 (R4 R5 + R2 (R4 + R5)) + R1 (R4 (R3 + R5) + R2 (R3 + R4 + R5))

>     }