The pair of equations `y = 0` and `y = -7` has

Options

A. one solution
B. two solutions
C. infinitely many solutions
D. no solution

Explanation

To solve the question regarding the pair of equations \( y = 0 \) and \( y = -7 \), we will analyze the equations step by step.

### Step-by-Step Solution:

1. **Understanding the Equations**:
- The equation \( y = 0 \) represents a horizontal line along the x-axis. This means that for any value of \( x \), the value of \( y \) is always 0.
- The equation \( y = -7 \) represents another horizontal line, which is located 7 units below the x-axis. For any value of \( x \), the value of \( y \) is always -7.

**Hint**: Remember that horizontal lines indicate that the y-coordinate remains constant regardless of the x-coordinate.

2. **Graphing the Equations**:
- On a graph, plot the line for \( y = 0 \) (the x-axis).
- Next, plot the line for \( y = -7 \). This line will run parallel to the x-axis, 7 units below it.

**Hint**: Use graph paper or a coordinate plane to visualize how these lines look. They will not cross each other.

3. **Analyzing the Lines**:
- Since both lines are horizontal and parallel, they will never intersect. This means that there are no points (x, y) that satisfy both equations simultaneously.

**Hint**: Parallel lines indicate that there is no solution where both equations hold true at the same time.

4. **Conclusion**:
- Therefore, we conclude that the pair of equations \( y = 0 \) and \( y = -7 \) have no solution in common.

**Final Statement**: The equations \( y = 0 \) and \( y = -7 \) are two parallel lines and do not intersect each other. Hence, they have no solution in common.