Solve the following system of equations graphically using your calculator.

To solve the given system of equations graphically using a calculator, you'll first want to rewrite the second equation in slope-intercept form (y = mx + b), which makes it easier to graph.

1. Start with the second equation:
\[ x - 2y = -6 \]

2. Rearranging it to solve for \(y\):
\[ -2y = -x - 6 \]
\[ y = \frac{1}{2}x + 3 \]

Now, we have two equations:
1. \( y = -x - 6 \)
2. \( y = \frac{1}{2}x + 3 \)

Next, you can plot these two equations on a graph.

### Steps to graph:
- **Graph the first equation:** \( y = -x - 6 \)
- This is a line with a slope of -1 and a y-intercept of -6.

- **Graph the second equation:** \( y = \frac{1}{2}x + 3 \)
- This is a line with a slope of \( \frac{1}{2} \) and a y-intercept of 3.

### Finding the intersection:
- The solution to the system is the point where the two lines intersect.

You should see where the two lines cross on your graph. This point of intersection will give you the values for \( x \) and \( y \) that solve the system of equations.

### Solution:
Using a graphing calculator or plotting the lines by hand, you will find the intersection point. This point is the solution to the system.

If you're unable to visualize the graph at the moment, you can find the intersection algebraically by setting the equations equal to each other:

\[
-x - 6 = \frac{1}{2}x + 3
\]

Solving this for \( x \):
\[
-x - \frac{1}{2}x = 3 + 6
\]
\[
-\frac{3}{2}x = 9
\]
\[
x = -6
\]

Substituting \( x = -6 \) back into either equation to find \( y \):
- Using \( y = -(-6) - 6 = 6 - 6 = 0 \)

Thus, **the solution to the system of equations is:**
\[
(x, y) = (-6, 0)
\]

This is the point where the two lines intersect on the graph.