When solving a linear system and obtaining a nonsensical result like $0 = 8$, it indicates that the system of equations has no solution because such an equation is inconsistent (impossible to satisfy). This typically happens when the two lines in the system are parallel, meaning they never intersect.

Looking at the answer choices:

• (a) "The system has one solution, (0, 8)" – This would indicate a single point of intersection, which does not align with the result $0 = 8$.
• (b) "The system has no solution" – This is correct because the nonsensical equation $0 = 8$ confirms that the lines are parallel and do not intersect.
• (c) "The system has one solution, (8, 0)" – This would also indicate a single point of intersection, which contradicts the result $0 = 8$.
• (d) "The system has an infinite number of solutions" – This would imply that the lines are identical (coincide entirely), which is not consistent with the result obtained.

Thus, the correct answer is (b) The system has no solution.

Would you like a detailed explanation of the substitution method or have any additional questions?

Here are five related questions for further exploration:

1. What are the characteristics of a linear system with infinitely many solutions?
2. How can we determine if two lines are parallel by examining their equations?
3. What other methods besides substitution can be used to solve systems of equations?
4. How can inconsistent results, like $0 = 8$, appear in systems solved by elimination?
5. What are real-world applications where systems of linear equations are used?

Tip: When solving systems, always double-check your result to see if it makes logical sense in terms of the system's graphical interpretation.