Python – Solve the Linear Equation of Multiple Variable

Prerequisite: Sympy.solve()

In this article, we will discuss how to solve a linear equation having more than one variable. For example, suppose we have two variables in the equations. Equations are as follows:

x+y =1

x-y =1

When we solve this equation we get x=1, y=0 as one of the solutions. In Python, we use Eq() method to create an equation from the expression. 

Syntax : Eq(expression,RHS value)

For example, if we have expression as x+y = 1. It can be written as Eq(x+y,1)

Solving equation with two variables

Construct the equations using Eq() method. To solve the equations pass them as a parameter to the solve() function.

Example :

Python3

# importing library sympy
from sympy import symbols, Eq, solve

# defining symbols used in equations
# or unknown variables
x, y = symbols('x,y')

# defining equations
eq1 = Eq((x+y), 1)
print("Equation 1:")
print(eq1)
eq2 = Eq((x-y), 1)
print("Equation 2")
print(eq2)

# solving the equation
print("Values of 2 unknown variable are as follows:")

print(solve((eq1, eq2), (x, y)))

Output:

Equation 1:
Eq(x + y, 1)
Equation 2
Eq(x - y, 1)
Values of 2 unknown variable are as follows:
{x: 1, y: 0} 

Solving equation with three variables

Construct the following equations using Eq() and solve then to find the unknown variables.

x +y+z =1

x+y+2z=1

Example: 

Python3

# importing library sympy
from sympy import symbols, Eq, solve

# defining symbols used in equations
# or unknown variables
x, y, z = symbols('x,y,z')

# defining equations
eq1 = Eq((x+y+z), 1)
print("Equation 1:")
print(eq1)

eq2 = Eq((x-y+2*z), 1)
print("Equation 2")
print(eq2)

eq3 = Eq((2*x-y+2*z), 1)
print("Equation 3")

# solving the equation and printing the
# value of unknown variables
print("Values of 3 unknown variable are as follows:")
print(solve((eq1, eq2, eq3), (x, y, z)))

Output:

Equation 1:
Eq(x + y + z, 1)
Equation 2
Eq(x - y + 2*z, 1)
Equation 3
Values of 3 unknown variable are as follows:
{x: 0, y: 1/3, z: 2/3}