the initial equation is:
[tex]\begin{gathered} x+y=5 \\ x-y=1 \end{gathered}[/tex]So we can add bout of the equation so:
[tex](x+y)+(x-y)=5+1[/tex]and we simplify it so:
[tex]\begin{gathered} x+x+y-y=6 \\ 2x=6 \end{gathered}[/tex]now we solve for x so:
[tex]\begin{gathered} x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]and with the value of x we can replace it in the first equation so:
[tex]3+y=5[/tex]and we solve for y:
[tex]\begin{gathered} y=5-3 \\ y=2 \end{gathered}[/tex]So the solution is x equal to 3 an y equal to 2
