Verified Answer :

\(\left\{\begin{array}{ccc}x+2y=5\\3x-y=1&/\cdot2\end{array}\right\\+\left\{\begin{array}{ccc}x+2y=5\\6x-2y=2\end{array}\right\\-----------\\. \ \ \ \ \ \ \ 7x=7\ \ \ \ /:7\\.\ \ \ \ \ \ \ x=1\\\\\left\{\begin{array}{ccc}x=1\\3x-y=1\end{array}\right\\\left\{\begin{array}{ccc}x=1\\3\cdot1-y=1\end{array}\right\\\left\{\begin{array}{ccc}x=1\\3-y=1\end{array}\right\\\left\{\begin{array}{ccc}x=1\\-y=1-3\end{array}\\\left\{\begin{array}{ccc}x=1\\-y=-2\end{array}\right\\\right\)
\(\left\{\begin{array}{ccc}x=1\\y=2\end{array}\right\\\)

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