Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.

Let's evaluate each expression in terms of whether it is rational or irrational, given that \( x \) and \( y \) are non-zero, rational numbers, and \( z \) is an irrational number.

1. **Expression: \( x + y \)**
- Since both \( x \) and \( y \) are rational numbers, their sum \( x + y \) is also a rational number.
- **Value: Rational**

2. **Expression: \( y + z \)**
- Here, \( y \) is a rational number and \( z \) is an irrational number. The sum of a rational number and an irrational number is always irrational.
- **Value: Irrational**

3. **Expression: \( xy \)**
- The product of two rational numbers \( x \) and \( y \) is also a rational number.
- **Value: Rational**

4. **Expression: \( xz \)**
- Here, \( x \) is a rational number and \( z \) is an irrational number. The product of a rational number and an irrational number is always irrational.
- **Value: Irrational**

Thus, the final classification of the values is:

| Expression | Value |
|------------|-----------|
| \( x + y \) | Rational |
| \( y + z \) | Irrational |
| \( xy \) | Rational |
| \( xz \) | Irrational |