The problem asks us to solve the following system of linear equations using either addition or subtraction: $ \begin{cases} -x + 6y = 9 \\ x + 6y = -3 \end{cases} $

1. Problem Description

The problem asks us to solve the following system of linear equations using either addition or subtraction:

$\begin{cases} -x + 6y = 9 \\ x + 6y = -3 \end{cases}$

2. Solution Steps

We can solve this system of equations using the addition method. Adding the two equations will eliminate the $x$ variable.

$(-x + 6y) + (x + 6y) = 9 + (-3)$

$-x + x + 6y + 6y = 6$

$12y = 6$

Now, we can solve for $y$:

$y = \frac{6}{12} = \frac{1}{2}$

Next, substitute the value of $y$ into either equation to solve for $x$. Let's use the second equation:

$x + 6y = -3$

$x + 6(\frac{1}{2}) = -3$

$x + 3 = -3$

$x = -3 - 3$

$x = -6$

Therefore, the solution is $x = -6$ and $y = \frac{1}{2}$.

3. Final Answer

$x = -6$, $y = \frac{1}{2}$