Circuit with 2 Batteries and 6 Resistors

1. The problem statement, all variables and given/known data

A circuit is constructed with six resistors and two batteries as shown. The battery voltages are V1 = 18 V and V2 = 12 V. The positive terminals are indicated with a + sign, The values for the resistors are: R1 = R5 = 73 Ω, R2 = R6 = 121 Ω R3 = 62 Ω, and R4 = 92 Ω. The positive directions for the currents I1, I2 and I3 are indicated by the directions of the arrows. What is V4, I1, I2, and I3?

2. Relevant equations

V=IR

3. The attempt at a solution
-I3R3+I1R1-ΔV1=0
+I6R6-ΔV2+I2R2+I1R1=0
-I1R1-I2R2-I5R5-I4R4-I6R6=0
-ΔV1-I3R3-I2R2+ΔV2-I6R6=0
-ΔV2-I5R5-I4R4=0
-I4R4-I6R6-ΔV1-I3R3-I2R2-I5R5=0

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