Okay, here we have this:
Considering the provided system, we are going to solve it using the elimination method, so we obtain the following:
[tex]\begin{gathered} \begin{bmatrix}6x-5y=41 \\ 2x+6y=6\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ (-3)2x+6y=6(-3)\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ -6x-18y=-18\end{bmatrix} \end{gathered}[/tex]Now we will add the equations to eliminate the y term:
[tex]\begin{gathered} \begin{bmatrix}-23y=23\end{bmatrix} \\ \begin{bmatrix}y=\frac{23}{-23}\end{bmatrix} \\ \begin{bmatrix}y=-1\end{bmatrix} \end{gathered}[/tex]Finally, let's replace in the first equation to find the value of x:
[tex]\begin{gathered} \begin{bmatrix}6x-5(-1)=41\end{bmatrix} \\ \begin{bmatrix}6x+5=41\end{bmatrix} \\ \begin{bmatrix}6x=36\end{bmatrix} \\ \begin{bmatrix}x=\frac{36}{6}\end{bmatrix} \\ \begin{bmatrix}x=6\end{bmatrix} \end{gathered}[/tex]Finally we obtain that the unique solution for the system is the ordered pair: (6, -1).
