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 sympyfrom sympy import symbols, Eq, solve # defining symbols used in equations# or unknown variablesx, y = symbols('x,y') # defining equationseq1 = Eq((x+y), 1)print("Equation 1:")print(eq1)eq2 = Eq((x-y), 1)print("Equation 2")print(eq2) # solving the equationprint("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 sympyfrom sympy import symbols, Eq, solve # defining symbols used in equations# or unknown variablesx, y, z = symbols('x,y,z') # defining equationseq1 = 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 variablesprint("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}
