[tex]elimination\ methode\\\\\underline{+\left\{\begin{array}{ccc}x+y=5\\x-y=7\end{array}\right}\ \ \ \ |add\ both\ sides\ of\ the\ equations\\.\ \ \ \ \ \ 2x=12\ \ \ \ \ |divide\ both\ sides\ by\ 2\\.\ \ \ \ \ \ \ \boxed{x=6}\\\\subtitute\ the\ value\ of\ x\ to\ the\ first\ equation:\\\\6+y=5\ \ \ \ |subtract\ 6\ from\ both\ sides\\\boxed{y=-1}\\\\Answer:\boxed{\left\{\begin{array}{ccc}x=6\\y=-1\end{array}\right}[/tex]