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diff --git a/solvers.py b/solvers.py
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+"""Routines for solving a linear system of equations."""
+
+import numpy as np
+from numpy.typing import NDArray
+
+
+def gaussian_eliminate(aa: NDArray[np.float_], bb: NDArray[np.float_]) -> NDArray[np.float_] | None:
+    """Solves a linear system of equations (Ax = b) by Gauss-elimination
+
+    Args:
+        aa: Matrix with the coefficients. Shape: (n, n).
+        bb: Right hand side of the equation. Shape: (n,)
+
+    Returns:
+        Vector xx with the solution of the linear equation or None
+        if the equations are linearly dependent.
+    """
+    nn = aa.shape[0]
+    xx = np.zeros((nn,), dtype=np.float_)
+    return xx