Question

Solve the system using the elimination methodWrite out the linear combination you preformed to eliminate one of the variables2m + n = 13m - 3n = 24

Answer 1

Solve using the elimination method;

$\begin{gathered} 2m+n=1---(1) \\ 3m-3n=24---(2) \\ \text{Multiply both equations by the coefficients of n} \\ \text{That is, multiply (1) by -3 and multiply (2) by 1} \\ -6m-3n=-3---(3) \\ 3m-3n=24---(4) \\ \text{Subtract equation (3) from (4)} \\ 9m=27 \\ \text{Divide both sides by 9} \\ m=3 \\ \text{Substitute for the value of m into equation (1)} \\ 2(3)+n=1 \\ 6+n=1 \\ n=1-6 \\ n=-5 \end{gathered}$

Therefore, m = 3 and n = -5