https://file.aiquickdraw.com/mathbot/file/1728063187113eyedhw2a.jpg

The problem shown in the image is asking to test for consistency and solve the following system of linear equations:

\[
\begin{aligned}
x + y + z &= 6 \\
x - y + 2z &= 5 \\
3x + y + z &= 8 \\
2x - 2y + 3z &= 7
\end{aligned}
\]

### Steps to Solve:

1. **Test for consistency** using the augmented matrix and row-reduce it to see if the system has a unique solution, infinitely many solutions, or no solution.

2. **Solve the system** by using any method such as:
   - **Gaussian elimination**
   - **Substitution**
   - **Matrix inversion** (if possible)
   - **Cramer's Rule**

Shall we proceed step-by-step with Gaussian elimination to test for consistency and solve this system?

Test for consistency and hence solve the system: x + y + z = 6; x - y + 2z = 5; 3x + y + z = 8; 2x - 2y + 3z = 7.

Learn how to test for consistency and solve the system of linear equations: x + y + z = 6, x - y + 2z = 5, 3x + y + z = 8, 2x - 2y + 3z = 7. This problem uses concepts from linear algebra, including Gaussian elimination and augmented matrix methods. Suitable for advanced high school and college students.

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