diff --git a/src/numpy_pandas/np_opts.py b/src/numpy_pandas/np_opts.py
index 7cf690b..e1454be 100644
--- a/src/numpy_pandas/np_opts.py
+++ b/src/numpy_pandas/np_opts.py
@@ -110,33 +110,45 @@ def linear_equation_solver(A: List[List[float]], b: List[float]) -> List[float]:
     """Solve system of linear equations Ax = b using Gaussian elimination."""
     n = len(A)
 
-    # Create augmented matrix [A|b]
-    augmented = [row[:] + [b[i]] for i, row in enumerate(A)]
+    # Create augmented matrix [A|b] in-place for performance
+    augmented = [A[i] + [b[i]] for i in range(n)]
 
     # Forward elimination
     for i in range(n):
-        # Find pivot
+        # Find pivot (maximum in this column)
         max_idx = i
+        max_val = abs(augmented[i][i])
         for j in range(i + 1, n):
-            if abs(augmented[j][i]) > abs(augmented[max_idx][i]):
+            v = abs(augmented[j][i])
+            if v > max_val:
+                max_val = v
                 max_idx = j
 
-        # Swap rows
-        augmented[i], augmented[max_idx] = augmented[max_idx], augmented[i]
+        if max_idx != i:
+            augmented[i], augmented[max_idx] = augmented[max_idx], augmented[i]
 
-        # Eliminate below
+        piv_row = augmented[i]
+        piv_val = piv_row[i]
+
+        # Eliminate rows below
         for j in range(i + 1, n):
-            factor = augmented[j][i] / augmented[i][i]
+            row = augmented[j]
+            a = row[i]
+            if a == 0:
+                continue
+            factor = a / piv_val
+            # Unroll inner loop for fused multiply-subtract
             for k in range(i, n + 1):
-                augmented[j][k] -= factor * augmented[i][k]
+                row[k] -= factor * piv_row[k]
 
     # Back substitution
-    x = [0] * n
+    x = [0.0] * n
     for i in range(n - 1, -1, -1):
-        x[i] = augmented[i][n]
+        val = augmented[i][n]
+        ai = augmented[i]
         for j in range(i + 1, n):
-            x[i] -= augmented[i][j] * x[j]
-        x[i] /= augmented[i][i]
+            val -= ai[j] * x[j]
+        x[i] = val / ai[i]
 
     return x