https://file.aiquickdraw.com/mathbot/file/1725962452863fvunmf1z.jpg

The system of linear equations in the image consists of two equations with three variables:

\[
E_1: 3x_1 + 2x_2 - 2x_3 = -1
\]
\[
E_2: x_1 - 4x_2 - 2x_3 = 9
\]

This is an underdetermined system (fewer equations than variables), so we can expect infinitely many solutions by expressing some variables in terms of others.

Would you like me to solve this system for \( x_1, x_2, \) and \( x_3 \) in terms of one of the variables (say, \( x_3 \))?

Let me know if you want further clarification or a different approach.

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Here are five related questions:
1. What are the characteristics of underdetermined systems?
2. How can parametric solutions be interpreted geometrically?
3. Can you explain how many solutions this system will have and why?
4. What methods can be used to solve systems of equations with more variables than equations?
5. How does Gaussian elimination work for solving systems of equations?

**Tip**: When solving a system of linear equations, organizing equations in matrix form can simplify the process.

Solve the system of equations: 3x1 + 2x2 - 2x3 = -1 and x1 - 4x2 - 2x3 = 9.

Solve the underdetermined system of equations: 3x1 + 2x2 - 2x3 = -1 and x1 - 4x2 - 2x3 = 9. This problem illustrates how to find solutions in systems where there are more variables than equations, using methods like substitution or Gaussian elimination.

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