The pair of linear equations y = 0 and y = -5 has:

Options

A. One solution
B. Two solutions
C. Infinitely many solutions
D. No solution

Answer

To solve the problem regarding the pair of linear equations \( y = 0 \) and \( y = -5 \), we will analyze the equations step by step.

### Step-by-Step Solution:

1. **Understand the Equations**:
The equations given are \( y = 0 \) and \( y = -5 \). The first equation represents the x-axis, where the value of y is always zero. The second equation represents a horizontal line where y is always -5.

**Hint**: Identify what each equation represents on the Cartesian plane.

2. **Graph the Equations**:
On a Cartesian plane, draw the x-axis and y-axis. The line \( y = 0 \) (the x-axis) will run horizontally through the origin (0,0). The line \( y = -5 \) will also run horizontally but will be positioned 5 units below the x-axis, crossing the y-axis at the point (0, -5).

**Hint**: Sketch both lines on the Cartesian plane to visualize their positions.

3. **Analyze the Lines**:
Since both lines are horizontal and parallel to each other (one at y = 0 and the other at y = -5), they will never intersect. This means there are no points (x, y) that satisfy both equations simultaneously.

**Hint**: Consider the geometric interpretation of parallel lines and their intersections.

4. **Conclusion**:
Since the two lines do not intersect, there are no solutions to the system of equations. Therefore, we conclude that the pair of linear equations has no solution.

**Hint**: Recall that two lines that do not meet indicate that there is no common solution.

### Final Answer:
The pair of linear equations \( y = 0 \) and \( y = -5 \) has **no solution**.