Form expressions using y, 2 and 7. Every expression must have y in it. Use only two number operations. These should be different.

Answer

To form expressions using \( y \), \( 2 \), and \( 7 \) with the requirement that each expression must include \( y \) and use only two different number operations, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables and Constants**: We have the variable \( y \) and the constants \( 2 \) and \( 7 \).

2. **Choose Operations**: We can use addition (+), subtraction (-), multiplication (×), and division (÷). We need to select two different operations.

3. **Form Expressions**:
- **Expression 1**: Use subtraction and addition.
- \( y - 2 = 7 \) (Subtracting 2 from \( y \))
- **Expression 2**: Use addition and subtraction.
- \( y - 7 = 2 \) (Subtracting 7 from \( y \))
- **Expression 3**: Use multiplication and division.
- \( \frac{y}{2} = 7 \) (Dividing \( y \) by 2)
- **Expression 4**: Use division and multiplication.
- \( \frac{y}{7} = 2 \) (Dividing \( y \) by 7)
- **Expression 5**: Use multiplication.
- \( 2y = 7 \) (Multiplying \( y \) by 2)
- **Expression 6**: Use multiplication.
- \( 7y = 2 \) (Multiplying \( y \) by 7)
- **Expression 7**: Use exponentiation.
- \( y = 2^7 \) (Raising 2 to the power of 7)
- **Expression 8**: Use exponentiation.
- \( y = 7^2 \) (Raising 7 to the power of 2)
- **Expression 9**: Use addition and multiplication.
- \( 2y + 7 \) (Adding 7 to \( 2y \))
- **Expression 10**: Use subtraction and multiplication.
- \( 2y - 7 \) (Subtracting 7 from \( 2y \))
- **Expression 11**: Use addition and multiplication.
- \( 7y + 2 \) (Adding 2 to \( 7y \))
- **Expression 12**: Use subtraction and multiplication.
- \( 7y - 2 \) (Subtracting 2 from \( 7y \))

### Summary of Expressions:
1. \( y - 2 = 7 \)
2. \( y - 7 = 2 \)
3. \( \frac{y}{2} = 7 \)
4. \( \frac{y}{7} = 2 \)
5. \( 2y = 7 \)
6. \( 7y = 2 \)
7. \( y = 2^7 \)
8. \( y = 7^2 \)
9. \( 2y + 7 \)
10. \( 2y - 7 \)
11. \( 7y + 2 \)
12. \( 7y - 2 \)