[tex]\left\{\begin{array}{ccc}18m+5n=-11\\12m+11n=31\end{array}\right\\\\elimination\ method\\\\\left\{\begin{array}{ccc}18m+5n=-11&|multiply\ both\ sides\ by\ 11\\12m+11n=31&|multiply\ both\ sides\ by\ (-5)\end{array}\right\\+\left\{\begin{array}{ccc}198m+55n=-121\\-60m-55n=-155\end{array}\right\ \ \ |add\ sides\ of\ the\ equations\\--------------\\.\ \ \ \ 138m=-276\ \ \ \ \ |divide\ both\ sides\ by\ 138\\.\ \ \ \ \ \ \ \ \ \boxed{m=-2}[/tex]
[tex]subtitute\ m=-2\ to\ one\ of\ the\ equations\ (I\ chose\ 18m+5n=-11)\\\\18\cdot(-2)+5n=-11\\-36+5n=-11\ \ \ \ \ \ \ |add\ 36\ to\ both\ sides\\5n=25\ \ \ \ \ \ \ |divide\ both\ sides\ by\ 5\\\boxed{n=5}[/tex]
[tex]Solution: \left\{\begin{array}{ccc}m=-2\\n=5\end{array}\right[/tex]
