[Tex/LaTex] Numbering each equation, and, have a large curly brace around them

Question

I can create a curly brace around a set of equations (aligned at two positions!) using aligned:

\begin{equation}
\left\{
\begin{aligned}[2]
    &\rho   &&= \frac{\e^{- \lambda_2 \H/k}}{\e^{1 + \lambda_1/k}}
    \\
    &\Tr{\rho} &&= 1 
    \\
    &\Tr{\rho \H} &&= \braket{E} 
\end{aligned}
\right.
\end{equation}

Or, I can create a set of equations where every line has a number, but no curly brace, using alignat:

\begin{alignat}{2}
    &\rho   &&= \frac{\e^{- \lambda_2 \H/k}}{\e^{1 + \lambda_1/k}}
    \\
    &\Tr{\rho} &&= 1 
    \\
    &\Tr{\rho \H} &&= \braket{E} 
\end{alignat}

How can I create a set of equations (still aligned at two positions) that all have numbers (like in the second example), and they also have a curly brace (like in the first example)??

Answer 1

It was pointed out that there exist a near duplicate to the question. However none of the answers there specifically address the situation where we have equations (and not conditions), and here the equations should be aligned at several points.

I was able to create the following solution after reading the answers in the near duplicate, using the empheq package, in combination with alignat.

\begin{empheq}[left={\empheqlbrace}]{alignat=2}
    &\rho &&= \frac{\e^{- \lambda_2 \H/k}}{\e^{1 + \lambda_1/k}}
    \\
    &\Tr{\rho} &&= 1 
    \\
    &\Tr{\rho \H} &&= \braket{E} 
\end{empheq}