How to Write a System of Equations in LaTeX

Why it happens

LaTeX has no single "system" command; you choose an environment by what the reader needs to see. cases gives the brace. align lines up the equals signs and numbers each line. systeme and alignat also line up the individual variables, which matters in a linear system with three or more unknowns, where the reader compares coefficients down each column.

Example

\usepackage{amsmath}
% Braced system:
\[
\begin{cases}
  x + y = 2 \\
  x - y = 0
\end{cases}
\]
% Aligned and numbered:
\begin{align}
  2x + y &= 5 \\
  x - 3y &= -2
\end{align}

Lining up the variables: systeme or alignat

With three or more unknowns, readers expect the x terms, the y terms and the z terms in columns, with a gap where a variable is missing. The systeme package does this automatically: list the equations separated by commas, and it aligns the terms, the signs and the equals signs and adds the left brace.

With only amsmath, alignat* gives the same layout by hand. Every term and every sign gets its own column. Write a sign that sits alone in a cell as {}+{}, so LaTeX still spaces it as a binary operator instead of a cramped unary sign.

\usepackage{amsmath}
\usepackage{systeme}
% in the document:
\[
\systeme{2x + 3y - z = 1, x - y + 4z = 6, 3x + 2z = 4}
\]

\begin{alignat*}{4}
  2x &{}+{}& 3y &{}-{}&  z &{}={}& 1 \\
   x &{}-{}&  y &{}+{}& 4z &{}={}& 6 \\
  3x &     &    &{}+{}& 2z &{}={}& 4
\end{alignat*}

A brace and a number on each equation

cases inside an equation environment gives the whole system one number, and align numbers every line but draws no brace. To have both, use empheq, which loads mathtools and amsmath. Its left option adds a brace to any amsmath environment, and each line keeps its own number and \label. numcases from the cases package is the other way to do it.

\usepackage{empheq}
% in the document:
\begin{empheq}[left=\empheqlbrace]{align}
  x + y &= 2 \label{eq:sum} \\
  x - y &= 0 \label{eq:diff}
\end{empheq}
Adding \eqref{eq:sum} and \eqref{eq:diff} gives $x = 1$.

Matrix form and augmented matrices

A linear system is often written as Ax = b. bmatrix (amsmath) draws square brackets and pmatrix round ones; columns are separated by & and rows by \\. For an augmented matrix with a vertical bar before the constants, use an array with | in its column specification, inside \left[ ... \right].

\usepackage{amsmath}
% in the document:
\[
\begin{bmatrix} 2 & 3 & -1 \\ 1 & -1 & 4 \\ 3 & 0 & 2 \end{bmatrix}
\begin{bmatrix} x \\ y \\ z \end{bmatrix}
=
\begin{bmatrix} 1 \\ 6 \\ 4 \end{bmatrix}
\qquad
\left[\begin{array}{rrr|r}
  2 &  3 & -1 & 1 \\
  1 & -1 &  4 & 6 \\
  3 &  0 &  2 & 4
\end{array}\right]
\]

Common errors

"Misplaced alignment tab character &": an & outside an alignment environment, for example in \[ ... \] without cases or aligned around it, or anywhere when amsmath is not loaded.

"Extra alignment tab has been changed to \cr": too many & on one row. cases has exactly two columns, so a second & in one row triggers it.

"Paragraph ended before \align was complete": a blank line inside align. Delete it, or put a lone % on that line.

"Missing $ inserted": cases or bmatrix used outside math mode. Wrap it in \[ ... \] or an equation environment.