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!

$$ \begin{cases} 4x+6y=96 \\\ x+y=20 \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 4x+6y=96 \\\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 4x+6(20-x)=96 \\\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 4x+120-6x=96 \\\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 120-2x=96 \\\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} -2x=96-120 \\\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 2x=24 \\\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} x=12 \\\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} x=12 \\\ y=20-12 \end{cases}\Longleftrightarrow $$ $$ \begin{cases} x=12 \\\ y=8 \end{cases} $$