So I'm a first time Latex learner and I'm still learning the roots, but I want to do something similar to the example given in the picture.
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\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\left\{
\begin{aligned}
y & = x\\
z & = a.
\end{aligned} \right.
\end{equation}
\end{document}
* EDIT *
As Werner commented, you can alternatively use the cases or dcases environments; the latter needs the mathtools package. The cases environment is really intended for the end of a line with something else in front.
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\left\{
\begin{aligned}
y & = x\\
z & = a.
\end{aligned} \right.
\end{equation}
\begin{equation}
\begin{dcases}
y = x\\
z = a.
\end{dcases}
\end{equation}
\end{document}
JPi
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I don't think cases is right unless there's something to the left of the {, like f(x)=... dcases works, but I've often had the need for the somewhat more flexible and general construct I used in the original example. – JPi Sep 17 '16 at 23:45

\[ \begin{cases} \ell_{1} : a_{1}x ... \\ \ell_{2} : a_{2}x ... ... \end{cases} \]. Unless of course you have any additional requirements – Au101 Sep 17 '16 at 23:03\[ \left\{ \begin{array}{l} \ell_{1} : a_{1}x ... ... ... \end{array} \right. \]– Au101 Sep 17 '16 at 23:05