Question

Please, how to solve this ?
18m + 5n = - 11
12m + 11n = 31

Answer 1

`18m + 5n = - 11\ /\cdot(-11)\\12m + 11n = 31\ /\cdot5\\\\-198m-55n=121\\60m+55n=155\\---------\\-198m+60m=121+155\\-138\ m=276/:(-138)\\m=-2\\\\18m+5n=-11\ \ \ \Rightarrow\ \ \ 18\cdot(-2)+5n=-11\\-36+5n=-11\\5n=-11+36\\5n=25\ /:5\\n=5\\\\ \left \{ {\big{m=-2} \atop \big{n=5}} \right.`

Answer 2

`\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}`


`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}`



`Solution: \left\{\begin{array}{ccc}m=-2\\n=5\end{array}\right`