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"

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