The Photon is telling you exactly what you use in order to have four equations and four unknowns. The fourth equation is \$I_0=I_3\$.
Using freely available SymPy and going clockwise for the mesh loops:
R1 = 4*RXR2 = 2*RXR3 = 8*RXR4 = 6*RXLoop1 = Eq( 0 + V1 - R1*(I1-I3) - R2*(I1-I2), 0 )Loop2 = Eq( 0 - R2*(I2-I1) - R3*(I2-I3) + 10*I0, 0 )Loop3 = Eq( 0 - R4*I3 - R3*(I3-I2) - R1*(I3-I1), 0 )Assign1 = Eq( I0, I3 )solve( [ Loop1, Loop2, Loop3, Assign1 ], [ I0, I1, I2, I3 ]){I0: V1/(6*RX - 10), I1: (29*RX*V1 - 20*V1)/(84*RX**2 - 140*RX), I2: (17*RX*V1 + 10*V1)/(84*RX**2 - 140*RX), I3: V1/(6*RX - 10)}Obviously, you know that \$V_1=10\:\text{V}\$ so you could just substitute that in and have only functions of \$R_x=R\$.
The missing equation is just what The Photon wrote in a short comment to you. That's all there was to remedying your quandary.