Systems of equations in LaTeX
A system of equations is a set of equations solved together; in LaTeX the cases environment braces them into a single block, with & marking the alignment point.
LaTeX command
\begin{cases} x + y = 2 \\ x - y = 0 \end{cases}Not the symbol you meant? Draw it to find the command →
The cases environment, from amsmath, draws a single large left brace and stacks its rows. Inside, \\ ends each line and & marks where the lines align, so \begin{cases} x + y = 2 \\ x - y = 0 \end{cases} sets two equations under one brace. It is the standard tool for both a system and a piecewise definition.
For a piecewise function the & separates the value from the condition, as in x for x >= 0 and -x otherwise. Because the condition is prose, wrap words in \text: write & \text{if } x > 0 so the words are upright and correctly spaced. The cases environment supplies only a left brace.
When you want the equations lined up on their equals signs without a brace, use the aligned environment: put an & just before each = and \\ between rows. aligned is meant to sit inside a display, so wrap it in . Both cases and aligned come from amsmath and are supported by KaTeX.
Other forms
\begin{aligned}...\end{aligned}align on the = signsExamples
$\begin{cases} x + y = 2 \\ x - y = 0 \end{cases}$a two-equation system under one brace
$|x| = \begin{cases} x & x \geq 0 \\ -x & x < 0 \end{cases}$a piecewise definition of absolute value
$f(n) = \begin{cases} 1 & \text{if } n = 0 \\ n \cdot f(n-1) & \text{if } n > 0 \end{cases}$a piecewise definition using \text for conditions
$$\begin{aligned} 2x + y &= 5 \\ x - y &= 1 \end{aligned}$$equations aligned on the equals sign, no brace
Tips and common mistakes
- cases and aligned both require amsmath; without it neither environment exists.
- In cases, & separates the value from its condition; each new line starts after \\.
- Wrap words in the condition in
\text{...}, e.g. &\text{if }x > 0, so they set upright with a proper leading space. - cases gives only a left brace. For a right brace use
\left....\right\}with an array, or the rcases environment from mathtools. - Use aligned when you want the equations lined up on = with no brace at all.
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Convert your maths to LaTeX →FAQ
How do I write a system of equations with a big brace?
Use the cases environment: \begin{cases} x + y = 2 \\ x - y = 0 \end{cases}. It draws the left brace automatically and stacks the rows. It needs amsmath.
How do I write a piecewise function?
Use cases with & before each condition: \begin{cases} x & \\ -x & x < 0 \end{cases}. Wrap any words in the condition in \text{...}.
How do I line up several equations on the equals sign?
Use the aligned environment inside a display, placing & just before each =: .