The problem describes a situation where, after solving a system of equations using substitution, you end up with a contradiction such as $3 = 2$. This indicates the system of equations is inconsistent, meaning the two equations represent lines that are parallel and never intersect.

Explanation:

• Parallel lines have the same slope but different $y$-intercepts.
• A contradiction like $3 = 2$ arises because there is no point of intersection, confirming that the lines do not cross each other.

What is true about the slope and $y$-intercepts of the lines?

1. The slopes of the two lines are the same.
2. The $y$-intercepts of the two lines are different.

Let me know if you would like a detailed explanation or examples to clarify further!

Questions for deeper understanding:

1. How do you determine when a system of equations is inconsistent?
2. Can you provide examples of equations representing parallel lines?
3. What does it mean geometrically when two lines have the same slope but different $y$-intercepts?
4. How does substitution help reveal inconsistencies in a system of equations?
5. What are other types of solutions (besides inconsistent) for a system of equations?