https://file.aiquickdraw.com/mathbot/file/17262499999635v2t0bx7.jpg

The image you uploaded contains a set of three equations generated using Kirchhoff's Current Law (KCL) at three nodes of an electrical circuit. The goal is to solve for the node voltages \(v_1\), \(v_2\), and \(v_3\).

Here are the equations extracted from the image:

1. \(-0.01 + \frac{v_1}{1000} + \frac{v_1 - v_2}{5000} + \frac{v_1 - v_3}{5000} = 0\)
2. \(\frac{v_2 - v_1}{1000} + \frac{v_2}{3000} + \frac{v_2 - v_3}{8000} = 0\)
3. \(\frac{v_3 - v_2}{8000} + \frac{v_3 - v_1}{5000} + \frac{v_3 - 120}{2000} = 0\)

The constants in these equations seem to correspond to resistances in ohms (e.g., 1000, 5000, 3000, etc.), and the values of \(i_s = 10 \text{mA}\) and \(v_s = 120 \text{V}\) are also provided as parameters of the circuit.

### Next Steps:
I can solve this system of equations using substitution or matrix methods (e.g., Gaussian elimination or Cramer's rule). Would you like me to proceed with solving it?

Here are some related questions to consider:
1. Would you like to see the step-by-step solution for this system of equations?
2. Are you familiar with using matrices to solve systems of equations?
3. Would you like more explanation on how these equations are derived from KCL?
4. Do you need a review of Kirchhoff's Current Law (KCL) and how it applies to circuits?
5. Would you like to explore how the current and voltage sources influence the node equations?

**Tip**: When solving circuits using KCL, always double-check unit consistency (e.g., ohms for resistance and amperes for current) to avoid calculation errors.

Give the values for the three node voltages that result from solving the three KCL equations, and remember to include the correct units. Recall that, in this circuit, i_s = 10 mA and v_s = 120 V. Supply the values for the three node voltages directly on the figure shown.

Learn how to solve for node voltages in an electrical circuit using Kirchhoff's Current Law (KCL). This problem involves setting up a system of linear equations based on KCL at three nodes and solving for the unknown voltages. Includes step-by-step instructions and key formulas such as Ohm's Law and matrix methods for solving systems of equations. Suitable for undergraduate electrical engineering students.

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