How to adjust the black splace between the top of the left curly brace and the begining of the contents

How to adjust the black splace between the top of the left curly brace and the begining of the contents

I want to type a system of equations delimited by the left curly brace. And I tried using the \left{ with aligned, and cases, and array, and numcases. But there are some difference between the results of these four methods. Here is the screen-shots and the source file:  \documentclass{article}
\usepackage{amsmath,amssymb}
      \usepackage{cases}
     \begin{document}
      \begin{align*}
     &\left\{\begin{aligned}
       &x=x,\\
        &u=u(x,t).
          \end{aligned}\right.  
          ~~~&& \begin{cases}
         x=x,\\
          u=u(x,t).
          \end{cases}
         ~~ &&
           \left\{\begin{array}{l}
         x=x,\\
      u=u(x,t).
        \end{array}\right.\\
      &\text{align} && \text{cases} &&\text{array}    
       \end{align*}

       using numcases:
      \begin{numcases}{}
        x=x,\nonumber\\
         u=u(x,t). \nonumber
                  \end{numcases}
      \end{document}
Sorry, I have trouble in including the command \documentclass{article} into the codes. My question is how can I adjust the space between the top tip of left curly brace and the first line of the equations, so that the results of using array etc is the same as that of using numcases. At present, I have no way of doing this.