The pair of linear equations y=0 and `y=-5` has _________ solutions .

Answer

To determine the number of solutions for the pair of linear equations \( y = 0 \) and \( y = -5 \), we can analyze the equations step by step.

### Step-by-Step Solution:

1. **Identify the Equations**:
- The first equation is \( y = 0 \).
- The second equation is \( y = -5 \).

2. **Graph the Equations**:
- The equation \( y = 0 \) represents the x-axis. This is a horizontal line where all points have a y-coordinate of 0.
- The equation \( y = -5 \) represents a horizontal line that is 5 units below the x-axis. This line consists of all points where the y-coordinate is -5.

3. **Analyze the Graph**:
- Since both equations are horizontal lines, they will never intersect.
- The line \( y = 0 \) (the x-axis) runs horizontally at y = 0, while the line \( y = -5 \) runs horizontally at y = -5.

4. **Determine the Number of Solutions**:
- Because the two lines are parallel and will never meet, there are no points (x, y) that satisfy both equations simultaneously.
- Therefore, the pair of linear equations has **no solutions**.

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

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