The Jacobi method solves a linear system Ax = b by iteratively updating each variable using the current values of all others. Starting from an initial guess, each component is updated as xᵢ⁽ᵏ⁺¹⁾ = (bᵢ − Σⱼ≠ᵢ aᵢⱼxⱼ⁽ᵏ⁾) / aᵢᵢ. Convergence is guaranteed when the matrix is strictly diagonally dominant.