# How to isolate one variable in an equation

## Description

Once we’ve expressed an equation or system of equations using the technique from how to write symbolic equations, we often want the software to isolate one variable in terms of all the others.

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## Using SymPy, in Python

This answer assumes you have imported SymPy as follows.

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from sympy import * # load all math functions
init_printing( use_latex='mathjax' ) # use pretty math output

Let’s create an equation with many variables.

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var('P V n R T')
ideal_gas_law = Eq( P*V, n*R*T )
ideal_gas_law

$\displaystyle P V = R T n$

To isolate one variable, call the `solve`

function, and pass that variable
as the second argument.

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solve( ideal_gas_law, R )

$\displaystyle \left[ \frac{P V}{T n}\right]$

The brackets surround a list of all solutions—in this case, just one. That solution is that $R=\frac{PV}{Tn}$.

Content last modified on 24 July 2023.

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