https://file.aiquickdraw.com/mathbot/file/1726286557447of00dfsx.jpg

The system of equations presented in the image is:

\[
\begin{aligned}
1. \, & x - z = 0 \\
2. \, & 2x - w = 0 \\
3. \, & y - w = 0
\end{aligned}
\]

### Step-by-Step Solution:

1. From equation \(x - z = 0\), we can express \(z\) in terms of \(x\): 
   \[
   z = x
   \]

2. From equation \(2x - w = 0\), we can express \(w\) in terms of \(x\): 
   \[
   w = 2x
   \]

3. From equation \(y - w = 0\), we can express \(y\) in terms of \(w\):
   \[
   y = w
   \]
   Substituting \(w = 2x\) from the previous step:
   \[
   y = 2x
   \]

### Final Values in Terms of \(x\):
- \(z = x\)
- \(w = 2x\)
- \(y = 2x\)

This system gives the relationships between the variables in terms of \(x\). Do you want more details or have any questions?

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Here are 5 follow-up questions:
1. What would the system look like if another equation involving \(x, y, z, w\) is added?
2. How do these solutions change if \(x = 0\)?
3. Can you create a matrix to represent this system of equations?
4. What happens if the second equation is modified to \(2x + w = 0\)?
5. What would a graphical interpretation of this system look like?

**Tip**: When solving a system of equations, start by simplifying and substituting step-by-step to avoid mistakes.

Solve the system of equations: x - z = 0, 2x - w = 0, y - w = 0.

Learn how to solve a system of three linear equations: x - z = 0, 2x - w = 0, and y - w = 0 using algebraic substitution. This problem covers key algebraic concepts such as solving systems of equations and variable substitution. Suitable for Grades 9-12.

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