# 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}```

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