1. Let's start by stating the problem: You have a system of equations: $$I_1 + 8I_2 + 3I_3 = -31$$ $$3I_1 - 2I_2 + I_3 = -5$$ $$2I_1 - 3I_2 + 2I_3 = 6$$ You are concerned about the signs in the equations, particularly why $I_2$'s sign is correct but the others seem wrong. 2. First, check each coefficient and constant term carefully. The sign of each term corresponds to how the currents $I_1$, $I_2$, $I_3$ affect the voltage or current sum in each equation. 3. The fact that $I_2$'s signs are correct and others are not may arise from an inconsistency in writing the equations based on the circuit or problem setup. You need to ensure that when you write the equations, the direction and reference polarity for each current and voltage is taken consistently. 4. To correct the signs for $I_1$ and $I_3$, reconsider the original circuit or equations derivation: - For example, if $I_1$ and $I_3$ are flowing in the opposite direction of assumed positive currents, their signs should be negative. - Conversely, if they flow as defined, the signs should be positive. 5. Check each term against the problem conditions or revisit Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) for sign conventions. Often, the sign errors come from mixing the direction of currents or voltage drops. 6. In conclusion, the sign correction depends on reviewing the physical meaning and directions in your equations, ensuring consistent use of signs relative to the chosen reference directions. 7. As a tip, label the currents' directions clearly on the circuit diagram, assign polarities, then write equations carefully respecting those signs to avoid errors. If you want, you can share the original circuit details, and I can help you write the correct signed equations.