Question

Solve the system of equations below using elimination by addition.3m - n = 11m - 3n = -15

Answer 1

Given the following System of equations:

$\begin{cases}3m-n=11 \\ m-3n=-15​\end{cases}$

You can solve it using the Elimination method as following:

1. You can multiply the first equation by -3.

2. Add the equations.

3. Solve for the variable "m".

Then:

$\begin{gathered} \begin{cases}-9m+3n=-33 \\ m-3n=-15​\end{cases} \\ ------------ \\ -8m=-48 \\ \\ m=\frac{-48}{-8} \\ \\ m=6 \end{gathered}$

4. Substitute the value of "m" into any original equation.

5. Solve for the variable "n".

Then:

$\begin{gathered} 3m-n=11 \\ 3(6)-n=11 \\ 18-n=11 \\ n=11-18 \\ n=-7 \end{gathered}$

The solution is:

$\begin{gathered} m=6 \\ n=-7 \end{gathered}$