Short Answer 
The system of equations consists of two equations: y = x + 8 and y = -2x – 1. By solving these equations simultaneously, we find that the solution is x = -3 and y = 5, represented graphically by the intersection point (-3, 5).
Step 1: Understand the System of Equations
The system of equations comprises two or more equations with the same set of unknowns that can be solved simultaneously. In this case, we have the following equations:
- Equation 1: y = x + 8
- Equation 2: y = -2x – 1
This setup allows us to find the values for the unknowns, x and y, that satisfy both equations at the same time.
Step 2: Solve the System of Equations
To find the solution for the system, we need to eliminate one variable by subtracting one equation from the other. Here’s how it’s done:
- Subtract Equation 2 from Equation 1: -2x – x – 1 – 8 = 0
- This simplifies to: -3x = 9
- Solving for x gives us: x = -3
Next, substitute x back into either equation to find y, which results in y = 5.
Step 3: Graphical Representation and Conclusion
The solution to the system of equations, where the lines intersect on a graph, is the point (-3, 5). This graphical intersection illustrates the common solution for both equations:
- Point of Intersection: (-3, 5)
- Conclusion: The simultaneous equations provide us with the values of x and y that satisfy both equations.
This confirms that the solution of the system of equations is indeed x = -3 and y = 5.