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\frac{1}{B_o} \, s_o + \frac{R_v}{B_g} \, s_g  = GF_O/\phi_n 

GF_O = V_e^{-1} \, \delta q_O + \left[ \frac{1}{B_{oi}} \, s_o + \frac{R_{vi}}{B_{gi}} \, s_{gi}  \right]

\frac{R_s}{B_o} \, s_o + \frac{1}{B_g} \, s_g  = GF_G/\phi_n

GF_G = V_e^{-1} \, \delta q_G + \left[ \frac{R_{si}}{B_{oi}} \, s_o + \frac{1}{B_{gi}} \, s_{gi}  \right]

 \frac{1}{B_w} \, s_w  = GF_W/\phi_n

GF_W  = V_e^{-1} \, \delta q_W + \frac{1}{B_{wi}} \, s_{wi} 

s_o = \frac{B_o \, (GF_oO - R_v \, GF_G)}{\phi_n \, (1- R_s \, R_v)} 

s_g = \frac{B_g \, (GF_G - R_s \, GF_O)}{\phi_n \, (1- R_s \, R_v)} 

s_w = \frac{B_w \, GF_W}{\phi_n} 

\frac{B_o \, (GF_oO - R_v \, GF_G)}{\phi_n \, (1- R_s \, R_v)} +  \frac{B_g \, (GF_G - R_s \, GF_O)}{\phi_n \, (1- R_s \, R_v)}  +  \frac{B_w \, GF_W}{\phi_n}  =1 

B_o \, (GF_oO - R_v \, GF_G) + B_g \, (GF_G - R_s \, GF_O)  + B_w \, GF_W \, (1- R_s \, R_v)  = \phi_n \, (1- R_s \, R_v)

(B_o - R_s \, B_g) \, GF_O +(B_g - R_V \, B_o) \, GF_G + (B_w  \, GF_W - \phi_n )\, (1- R_s \, R_v)  = 0