The pair of equations `x = 0` and `x = -4` has ______ solution.

Options

A. a unique solution
B. no solution
C. infinitely many solution
D. only solution (0,0)

Answer

To determine how many solutions the pair of equations \( x = 0 \) and \( x = -4 \) has, we can analyze the equations graphically and algebraically.

### Step-by-Step Solution:

1. **Understanding the Equations**:
- The first equation is \( x = 0 \). This represents a vertical line on the y-axis where all points have an x-coordinate of 0.
- The second equation is \( x = -4 \). This represents another vertical line where all points have an x-coordinate of -4.

2. **Graphing the Equations**:
- On a coordinate plane, draw the x-axis (horizontal) and y-axis (vertical).
- The line \( x = 0 \) is the y-axis itself.
- The line \( x = -4 \) is a vertical line that is 4 units to the left of the y-axis.

3. **Analyzing the Lines**:
- Since both equations represent vertical lines, we need to check if these lines intersect.
- The line \( x = 0 \) (y-axis) and the line \( x = -4 \) are parallel lines.

4. **Conclusion**:
- Parallel lines do not intersect at any point. Therefore, there are no solutions to the pair of equations.
- Hence, the pair of equations \( x = 0 \) and \( x = -4 \) has **0 solutions**.

### Final Answer:
The pair of equations \( x = 0 \) and \( x = -4 \) has **0 solutions**.