To determine the number of solutions to a nonlinear system, we need to consider the nature of the equations involved. Let’s analyze the possibilities step by step.

Solution By Steps

Step 1: Identify the Type of Nonlinear System

Nonlinear systems can have various forms, such as no solution, one solution, or multiple solutions. We need to analyze the given system to determine its nature.

Step 2: Analyze the System

If the system has contradictory equations (e.g., 0 = 1), it has no solution. If the equations are equivalent (e.g., 0 = 0), it has infinitely many solutions. If the equations are distinct and consistent, it has one unique solution.

Step 3: Conclusion

Based on the analysis, if the system has distinct and consistent equations, it will have one unique solution. Therefore, the correct answer is:

Final Answer

B. One solution

Summary

Understanding the nature of a nonlinear system is crucial in determining the number of solutions it possesses. By analyzing the consistency and distinctiveness of the equations involved, we can ascertain whether the system has no solution, one solution, or multiple solutions. This knowledge is essential in various fields, including mathematics, engineering, and physics, where nonlinear systems frequently arise and require precise solution methods.