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The system of equations presented is:

\[
\begin{aligned}
2w - x + y - z &= 2 \\
w + x - y + 2z &= 3 \\
3w + z &= 5 \\
3w - 3x + 3y - 4z &= 1
\end{aligned}
\]

We need to express \(w\) and \(x\) in terms of \(y\) and \(z\).

### Step 1: Solve for \(w\) in terms of \(z\)
From the third equation \(3w + z = 5\), solve for \(w\):

\[
3w = 5 - z
\]
\[
w = \frac{5 - z}{3}
\]

### Step 2: Substitute \(w\) into the other equations
Substitute \(w = \frac{5 - z}{3}\) into the first, second, and fourth equations.

#### First equation:
\[
2\left(\frac{5 - z}{3}\right) - x + y - z = 2
\]
Multiply by 3 to eliminate the fraction:
\[
2(5 - z) - 3x + 3y - 3z = 6
\]
Simplify:
\[
10 - 2z - 3x + 3y - 3z = 6
\]
\[
-3x + 3y - 5z = -4
\]
\[
x = y - \frac{5z}{3} + \frac{4}{3}
\]

So, \(x\) is expressed in terms of \(y\) and \(z\).

Thus, the solutions are:

\[
w = \frac{5 - z}{3}, \quad x = y - \frac{5z}{3} + \frac{4}{3}
\]

Would you like further details or explanations? Here are a few related questions for deeper understanding:

1. How can you verify that these expressions for \(w\) and \(x\) satisfy all the original equations?
2. How do infinite solutions occur in systems of linear equations?
3. What is the geometric interpretation of a system with infinite solutions?
4. How does substituting variables affect the number of solutions in a system?
5. How would you find the solution for specific values of \(y\) and \(z\)?

**Tip:** For systems with infinite solutions, parameterizing variables in terms of others simplifies understanding the solution set.

The following system has an infinite number of solutions. Write the solution in terms of y and z.
2w - x + y - z = 2
w + x - y + 2z = 3
3w + z = 5
3w - 3x + 3y - 4z = 1

This problem involves solving a system of linear equations with infinite solutions. Learn how to express w and x in terms of y and z using substitution, and understand the method behind finding these solutions. Ideal for students in grades 9-12.

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