Here is the graphical representation of the system of equations:

• The blue line represents $y = x + 3$.
• The red line represents $y = -2x - 6$.
• The intersection point, marked in green, is at $(-3, 0)$.

This point is the solution to the system of equations, where both equations are satisfied.

Would you like more details or have any questions about this? Here are some related questions to explore:

1. What happens to the solution if the slopes of the two lines are the same?
2. How can you determine the number of solutions a system of linear equations has based on their graphs?
3. What is the algebraic method to solve systems of equations?
4. How do you find the point of intersection using substitution or elimination methods?
5. How can the slope and y-intercept of a line affect its graph?

Tip: When graphing lines, always check the slope and intercepts carefully to ensure accurate plotting!