can you explain me step by step how to solve this equations of 2 variables" x+y=170,x-y=20"

can you explain me step by step how to solve this equations of 2 variables" x+y=170,x-y=20"

$$\small{\text{$
\begin{array}{lrclrclr}
(1) &\qquad x &+& y &=& 170\\
(2) &\qquad x &-& y &=& 20 \\
\hline
(1)+(2) & \qquad x+x &+&y-y &=& 170+20\\
& \qquad x+x &+&0 &=& 170+20\\
& \qquad 2x &+&0 &=& 170+20\\
& \qquad 2x &+&0 &=& 190\\
& \qquad 2x && &=& 190 &\qquad | \qquad :2\\
& \qquad \textcolor[rgb]{1,0,0}{x} &&&\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{95}\\
\hline
(1) &\qquad x &+& y &=& 170\\
&\qquad 95 &+& y &=& 170\\
&\qquad 95 &+& y &=& 170&\qquad | \qquad -95\\
&\qquad & & y &=& 170-95 \\
& \qquad && \textcolor[rgb]{1,0,0}{y} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{75}\\
\end{array}
$}}$$