align two piecewise functions

Question

I have problem with my piecewise functions

I read others post and I tried this but I have errors

\documentclass{article}
\usepackage{amsmath}
\begin{document}
    \begin{align*}
    $x_{{i}{j}}$ = 
         &\begin{cases}
           \text{1,} &\quad\text{Si se envía agua desde área i ( i $\in$   \{1,2,3,4,5,6,7,8,9,10\}) a sitio j ( j $\in$  \{1,2,3,4,5,6,7\})} \\
           \text{0,} &\quad\text{En caso contrario}
         \end{cases}\\
    $y_{j}$ = 
         &\begin{cases}
           \text{1,} &\quad\text{  Si se construye planta en el sitio j ( j $\in $   \{1,2,3,4,5,6,7\})} \\
           \text{0,} &\quad\text{En caso contrario}
         \end{cases}
    \end{align*}
\end{document}

Runaway argument? ! Paragraph ended before \align* was complete. \par l.592

I did this (using [) and it works well but they appear not aligned

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[   
x_{{i}{j}} = 
     \begin{cases}
       \text{1,} &\quad\text{Si se envía agua desde área i ( i $\in$   \{1,2,3,4,5,6,7,8,9,10\}) a sitio j ( j $\in$  \{1,2,3,4,5,6,7\})} \\
       \text{0,} &\quad\text{En caso contrario}
     \end{cases}
\]
\[   
y_{j} = 
     \begin{cases}
       \text{1,} &\quad\text{  Si se construye planta en el sitio j ( j $\in $   \{1,2,3,4,5,6,7\})} \\
       \text{0,} &\quad\text{En caso contrario}
     \end{cases}
\]


\end{document}

and I want they are aligned, like this

Answer 1

Beware! align already typesets its contents in math mode (but \text reverts to text mode).

You have to just align the equals signs with &=; for the long line, I suggest a tabular. Some vertical spacing will help, too.

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align*}
x_{ij} &=
  \begin{cases}
  1, &\begin{tabular}[t]{@{}l@{}}
      Si se envía agua desde área $i$ ($i\in\{1,2,3,4,5,6,7,8,9,10\}$) \\
      a sitio $j$ ($j\in\{1,2,3,4,5,6,7\}$)
      \end{tabular} \\[4ex]
  0, &\text{En caso contrario}
\end{cases}\\
y_{j} &=
  \begin{cases}
  1, &\text{Si se construye planta en el sitio $j$ ($j\in\{1,2,3,4,5,6,7\}$)} \\[1ex]
  0, &\text{En caso contrario}
  \end{cases}
\end{align*}

\end{document}

Answer 2

Here it is I simplified the text part typing using the cases* environment from mathtols (needless to load àmsmath`). I had to dplit the first case to make it fit the margins:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[showframe]{geometry}
\usepackage{mathtools}

\begin{document}

    \begin{align*}
    x_{{i}{j}} & =
         \begin{cases*}
           \text{1,} &\quad Si se envía agua desde área $ i\: ( i \in \{1,2,3,4,5,6,7,8,9,10\})$ \\
             & \quad a sitio $ j\: ( j \in \{1,2,3,4,5,6,7\})$ \\
           \text{0,} &\quad{En caso contrario}
         \end{cases*}\\[1.5ex]
   y_{j} & =
   \begin{cases*}
 1, &\quad Si se construye planta en el sitio $ j\: ( j \in \{1,2,3,4,5,6,7\})$ \\
 0, &\quad En caso contrario
 \end{cases*}
    \end{align*}

\end{document} 

Answer 3

If we go back to your original attempt, a few quick changes gives the result you wanted. This: removes the $$ around x_{ij} and y_j and moves the & you use for alignment to align the equals signs. Edit: I also compressed the set notation to shorten the long line and returned i and j to math mode, as you currently have them as subscripts in math mode. If you'd prefer them to be set upright you should change the subscripts as well.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
x_{ij} &=
\begin{cases}
\text{1,} &\quad\text{Si se envía agua desde área $i$ ($i \in \{1,2,\dots,10\}$) a sitio $j$ ($j \in \{1,2,\dots,7\}$)} \\
\text{0,} &\quad\text{En caso contrario}
\end{cases}\\
y_{j} &= 
\begin{cases}
\text{1,} &\quad\text{  Si se construye planta en el sitio $j$ ($j \in \{1,2,\dots,7\}$)} \\
\text{0,} &\quad\text{En caso contrario}
\end{cases}
\end{align*}
\end{document}

Output: