This paper introduces a randomized version of the Kaczmarz algorithm for solving consistent, overdetermined linear systems. The algorithm converges with an expected exponential rate, and its convergence rate depends only on the scaled condition number of the matrix, not on the number of equations. This makes it more efficient than previously known methods, especially for extremely overdetermined systems. The algorithm selects rows of the matrix with probability proportional to the square of their Euclidean norm, which improves convergence. Theoretical analysis and numerical simulations show that the randomized Kaczmarz method can converge faster than the conjugate gradient algorithm, even for moderately overdetermined systems. The method is also effective for reconstructing bandlimited functions from nonuniform sampling. The paper also discusses the optimality of the algorithm and its performance on random Gaussian matrices. Numerical experiments demonstrate that the randomized Kaczmarz method outperforms the conjugate gradient algorithm in terms of computational efficiency for certain cases. The algorithm is shown to be effective for both consistent and inconsistent systems, and further improvements, such as the use of relaxation parameters, are discussed.This paper introduces a randomized version of the Kaczmarz algorithm for solving consistent, overdetermined linear systems. The algorithm converges with an expected exponential rate, and its convergence rate depends only on the scaled condition number of the matrix, not on the number of equations. This makes it more efficient than previously known methods, especially for extremely overdetermined systems. The algorithm selects rows of the matrix with probability proportional to the square of their Euclidean norm, which improves convergence. Theoretical analysis and numerical simulations show that the randomized Kaczmarz method can converge faster than the conjugate gradient algorithm, even for moderately overdetermined systems. The method is also effective for reconstructing bandlimited functions from nonuniform sampling. The paper also discusses the optimality of the algorithm and its performance on random Gaussian matrices. Numerical experiments demonstrate that the randomized Kaczmarz method outperforms the conjugate gradient algorithm in terms of computational efficiency for certain cases. The algorithm is shown to be effective for both consistent and inconsistent systems, and further improvements, such as the use of relaxation parameters, are discussed.