The equation you provided is:

\[
x + 2y - z = 5
\]

This is a linear equation in three variables: \( x \), \( y \), and \( z \). Since there are three variables but only one equation, it's underdetermined, meaning there are infinitely many solutions depending on the values of two of the variables.

You can express one variable in terms of the other two. For example, solving for \( x \):

\[
x = 5 - 2y + z
\]

This shows that \( x \) depends on the values of \( y \) and \( z \).

Alternatively, you could solve for \( y \) or \( z \), depending on which variable you want to isolate.

Would you like to solve for a different variable or explore how this equation behaves graphically?

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Here are some related questions you might find interesting:
1. How do we graph a plane given a linear equation in three variables?
2. What happens if we add another equation to this system?
3. Can we solve this system if one of the variables is given a fixed value?
4. How does this equation represent a plane in 3D space?
5. What are the methods to solve systems of linear equations with more than one equation?

**Tip**: For a system with more variables than equations, you usually express some variables in terms of others.

Learn how to solve the linear equation x + 2y - z = 5, a system with three variables. Understand how underdetermined systems work and how to express one variable in terms of others. Suitable for students in Grades 10-12.

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