Question

Solve the following system using the elimination method. Enter your answer as an ordered pair in the form (x,y) If there is one unique solution. Enter all if there are infinitely many solutions and enter none if there are no solutions 6x - 5y = 41 2x + 6y = 6

Answer 1

Okay, here we have this:

Considering the provided system, we are going to solve it using the elimination method, so we obtain the following:

`\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}`

Now we will add the equations to eliminate the y term:

`\begin{gathered} \begin{bmatrix}-23y=23\end{bmatrix} \\ \begin{bmatrix}y=(23)/(-23)\end{bmatrix} \\ \begin{bmatrix}y=-1\end{bmatrix} \end{gathered}`

Finally, let's replace in the first equation to find the value of x:

`\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=(36)/(6)\end{bmatrix} \\ \begin{bmatrix}x=6\end{bmatrix} \end{gathered}`

Finally we obtain that the unique solution for the system is the ordered pair: (6, -1).