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+# Solving non-linear equations
+
+## Introduction
+
+
+## Prerequisites
+
+```python
+import numpy
+import scipy
+import sympy
+```
+
+
+## fsolve from SciPy 
+
+```python
+from scipy.optimize import fsolve
+
+def equations(vars):
+    x, y = vars
+    eq1 = x**2 + y**2 - 25
+    eq2 = x**2 - y
+    return [eq1, eq2]
+
+initial_guess = [1, 1]
+solution = fsolve(equations, initial_guess)
+print("Solution:", solution)
+```
+
+## root from SciPy
+```python
+from scipy.optimize import root
+
+def equations(vars):
+    x, y = vars
+    eq1 = x**2 + y**2 - 25
+    eq2 = x**2 - y
+    return [eq1, eq2]
+
+initial_guess = [1, 1]
+solution = root(equations, initial_guess)
+print("Solution:", solution.x)
+```
+
+
+## minimize from SciPy
+```python
+from scipy.optimize import minimize
+
+# Define the equations
+def equation1(x, y):
+    return x**2 + y**2 - 25
+
+def equation2(x, y):
+    return x**2 - y
+
+# Define the objective function for optimization
+def objective(xy):
+    x, y = xy
+    return equation1(x, y)**2 + equation2(x, y)**2
+
+# Initial guess
+initial_guess = [1, 1]
+
+# Perform optimization
+result = minimize(objective, initial_guess)
+solution_optimization = result.x
+
+print("Optimization Method Solution:", solution_optimization)
+
+```
+
+## nsolve from SymPy
+```python
+from sympy import symbols, Eq, nsolve
+
+# Define the variables
+x, y = symbols('x y')
+
+# Define the equations
+eq1 = Eq(x**2 + y**2, 25)
+eq2 = Eq(x - y, 0)
+
+# Initial guess for the solution
+initial_guess = [1, 1]
+
+# Use nsolve to find the solution
+solution = nsolve([eq1, eq2], [x, y], initial_guess)
+print("Solution:", solution)
+```
+
+## newton_method from NumPy
+
+```python
+import numpy as np
+
+def equations(vars):
+    x, y = vars
+    eq1 = x**2 + y**2 - 25
+    eq2 = x**2 - y
+    return np.array([eq1, eq2])
+
+def newton_method(initial_guess, tolerance=1e-6, max_iter=100):
+    vars = np.array(initial_guess, dtype=float)
+    for _ in range(max_iter):
+        J = np.array([[2 * vars[0], 2 * vars[1]], [2 * vars[0], -1]])
+        F = equations(vars)
+        delta = np.linalg.solve(J, -F)
+        vars += delta
+        if np.linalg.norm(delta) < tolerance:
+            return vars
+
+initial_guess = [1, 1]
+solution = newton_method(initial_guess)
+print("Solution:", solution)
+```
+\ No newline at end of file