or

To solve the system of equations by graphing, we have the following equations to work with:

1. \( y = -6x \)
2. \( y = -7x - 1 \)

Step 1: Graph the equations

Graph of the first equation \( y = -6x \):

• The slope is -6 and the y-intercept is 0.
• Plot two points:
  • When \( x = 0 \), \( y = 0 \) (the y-intercept).
  • When \( x = 1 \), \( y = -6 \) (point (1, -6)).
• Draw a straight line through these points.

Graph of the second equation \( y = -7x - 1 \):

• The slope is -7 and the y-intercept is -1.
• Plot two points:
  • When \( x = 0 \), \( y = -1 \) (the y-intercept).
  • When \( x = 1 \), \( y = -8 \) (point (1, -8)).
• Draw a straight line through these points.

Step 2: Find the intersection point

Once you have the lines graphed, you look for the point where they intersect.

Finding the Solution Algebraically

To find the solution numerically (for confirmation), set the equations equal to each other:

\[ -6x = -7x - 1 \]

Now solve for \( x \):

\[ -6x + 7x = -1 \] \[ x = -1 \]

Now substitute \( x = -1 \) back into either equation to find \( y \):

Using the first equation: \[ y = -6(-1) = 6 \]

Solution

The solution (intersection point) is: \[ (x, y) = (-1, 6) \]

So, the solution to the system of equations is:

\[ \boxed{(-1, 6)} \]