[tex]Elimination\ method:\\ \left\{\begin{array}{ccc}2x+y=5\\x+3y=5&|multiply\ both\ sides\ by\ (-2)\end{array}\right\\+\left\{\begin{array}{ccc}2x+y=5\\-2x-6y=-10\end{array}\right\ \ \ |add\ sides\ of\ the\ equations\\------------\\.\ \ \ \ -5y=-5\ \ \ \ \ |divide\ both\ sides\ by\ (-5)\\.\ \ \ \ \ \ \ \boxed{y=1}\\\\substitute\ the\ value\ of\ y\ into\ one\ of\ the\ equations\ (\#2)\\\\x+3\times1=5\\x+3=5\ \ \ \ \ \ |subtract\ 3\ from\ both\ sides\\\boxed{x=2}\\\center\boxed{Answer:x=2\ and\ y=1\to(2;\ 1)}[/tex]
