Can't get to solve this word problem Price of lemon juice bottle is $4$ , price of orange juice bottle is $6$.
A buyer bought $20$ bottles and the total cost is $96$. 
How many lemon bottles and orange bottles did the buyer get? 
I know the answer but I don't know the steps to get to it.

The way of getting this system is explained by others, I gonna help with solving that system!
$$
\begin{cases}
4x+6y=96 \\
x+y=20
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
4x+6y=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
4x+6(20-x)=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
4x+120-6x=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
120-2x=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
-2x=96-120 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
2x=24 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
x=12 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
x=12 \\
y=20-12
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
x=12 \\
y=8
\end{cases}
$$
