Please, how do you solve this system of equations?
\[
18m + 5n = -11
\]
\[
12m + 11n = 31
\]
Answer (3)
\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}
s u b t i t u t e m = − 2 t o o n e o f t h e e q u a t i o n s ( I c h ose 18 m + 5 n = − 11 ) 18 ⋅ ( − 2 ) + 5 n = − 11 − 36 + 5 n = − 11 ∣ a dd 36 t o b o t h s i d es 5 n = 25 ∣ d i v i d e b o t h s i d es b y 5 n = 5
Solution: \left\{\begin{array}{ccc}m=-2\
=5\end{array}\right
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\
=5\\\\ \left \{ {\big{m=-2} \atop \big{n=5}} \right.
To solve the system of equations, use the elimination method by aligning the coefficients and combining the equations to find values for m and n. After substitution, we find that m = -2 and n = 5. Thus, the solution is {m = -2, n = 5}.
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