input: 
  def solve_linear_equation_system(a: int, b: int, c: int) -> (float, float):
      """
      Solve a linear equation system of the form: ax + by = c.
  
      >>> solve_linear_equation_system(2, 1, 4)
      (2.0, 2.0)
      >>> solve_linear_equation_system(3, 4, 10)
      (2.6666666666666665, 1.0)
      """
  
  
  以下是针对题目内容的英文提问：
  
  
  **Question:** 
  How would you implement a Python function named `solve_linear_equation_system` that solves a linear equation system of the form \( ax + by = c \)? The function should take three integer parameters (a, b, c) and return a tuple containing the values of x and y that satisfy the equation. Additionally, describe how you would test this function ensuring correctness?
  
output:     if a == 0 and b == 0:
          raise ValueError("Both coefficients a and b cannot be zero.")
      if a == 0:
          return (float('inf'), c / b)
      if b == 0:
          return (c / a, float('inf'))
      x = c / a
      y = 0
      return (x, y)