# Equations

## Equations

You can define equations using SymPy using 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 [1]:
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

$

In [2]:
x, y = symbols('x y')
eq2 = 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 [3]:
x, y, z = symbols('x y z')
eq2 = 2*y - x -5
eq3 = eq2.subs(x,z)
eq3


Out[3]:
2*y - z - 5