# Equations

## Equations

You can define equations in Python using SymPy and symbolic math variables. Equations in SymPy are different than expressions. An expression does not have equality. An expression is a collection of symbols and operators, but expressions are not equal to anything. Equations have equality. An equation can be thought of as an expression equal to something else.

A code section that defines the equation $4x + 2 = 0$ is below. Note all equations defined in SymPy are assumed to equal zero.

In :
from sympy import symbols, Eq
x = symbols('x')
eq1 = Eq(4*x + 2)


If you want to define the equation $2y - x = 5$, which is not equal to zero, you just have to subtract the right hand side of the equation from the left hand side of the equation first.

2y - x = 5
2y - x -5 = 0
In :
x, y = symbols('x y')

eq2 = Eq(2*y - x - 5)


Alternatively, an equation can be defined with a left hand side and a right hand side passed as separate arguments.

In :
x, y = symbols('x y')
eq2 = Eq(2*y - x, 5)


### Substitutions in Equations

Symbols and expressions can be substituted into equations. In the code section below, the variable $z$ is substituted in for the variable $x$ ($z$ replaces $x$).

In :
x, y, z = symbols('x y z')
eq2 = Eq(2*y - x - 5)
eq3 = eq2.subs(x,z)
eq3


Out:
Eq(2*y - z - 5, 0)