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The solution to the system of equations is:

\[
x = \frac{-17}{66}, \quad y = \frac{87}{44}, \quad z = \frac{-59}{132}
\]

Would you like more details on how these results were derived or explanations of any specific steps?

Here are 5 related questions you could explore:
1. How can we interpret these fractions in decimal form?
2. How would the system change if one equation was altered, for example, \(4y - 2z = 8 - 7x\)?
3. Can this system be solved using a different method, like substitution or elimination?
4. What happens if you graph these equations in 3D space?
5. Can you verify this solution by substituting the values back into the original equations?

**Tip:** When solving systems of linear equations, always check for consistency (whether the system has one solution, no solution, or infinitely many solutions).

Solve for variables in the system of equations: x - 5z = y, 2x = 3y + z - 6, 4y - 2z = 7 - 7x.

This solution explains how to solve the system of equations: x - 5z = y, 2x = 3y + z - 6, and 4y - 2z = 7 - 7x. Learn how to find x, y, and z using algebraic methods such as substitution or elimination. Suitable for high school students in Grades 10-12.

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