How to solve a pair of nonlinear equations?

Learn, how to solve a pair of nonlinear equations using Python? By Pranit Sharma Last updated : October 10, 2023

NumPy is an abbreviated form of Numerical Python. It is used for different types of scientific operations in python. Numpy is a vast library in python which is used for almost every kind of scientific or mathematical operation. It is itself an array which is a collection of various methods and functions for processing the arrays.

Solving a pair of nonlinear equations

For this purpose, we will use the fsolve() method from optimize module of scipy. This method finds the roots of a function. It returns the roots of the (non-linear) equations defined by func(x) = 0 given a starting estimate.

Syntax:

scipy.optimize.fsolve(func, x0, args=())

Parameter(s):

funccallable f(x, *args): A function that takes at least one (possibly vector) argument, and returns a value of the same length.
x0ndarray: The starting estimate for the roots of func(x) = 0.
argstuple, optional: Any extra arguments to func.

Let us understand with the help of an example,

Python program to solve a pair of nonlinear equations

# Importing fsolve method
from scipy.optimize import fsolve

# Import math
import math

# Defining a function for solving equation 
# for some values of x and y
def fun(k):
    x, y = k
    return (x+y**2-4, math.exp(x) + x*y - 3)

# Calling function
x, y =  fsolve(fun, (1, 1))

# Display result
print("Result:\n",fun((x,y)))