To determine the number of solutions to the pair of equations \( x = 0 \) and \( x = -4 \), let's analyze each equation one by one.
1. Equation 1: \( x = 0 \)
- This equation states that \( x \) must be 0.
2. Equation 2: \( x = -4 \)
- This equation states that \( x \) must be -4.
Now, for a solution to satisfy both equations simultaneously, the value of \( x \) must satisfy both \( x = 0 \) and \( x = -4 \) at the same time. However, this is not possible, because:
- If \( x \) is 0, it cannot be -4.
- If \( x \) is -4, it cannot be 0.
Therefore, there is no value of \( x \) that can satisfy both \( x = 0 \) and \( x = -4 \) simultaneously. As a result, the pair of equations \( x = 0 \) and \( x = -4 \) has no solution.
Hence, the correct answer is:
b) no solution
