When you end up with an expression like $0 = 4$ after simplifying a system of equations, this indicates that there is a contradiction. Such an expression cannot be true, because 0 is never equal to 4.

What this means for the lines:

• The lines are parallel. When two lines are parallel, they never intersect, which means they have no point in common.
• This implies that the system of equations has no solution.

In other words, the system of equations is inconsistent. The equations represent two lines that do not intersect.

Key Points:

• The contradiction $0 = 4$ suggests the system is inconsistent.
• The lines represented by the system are parallel and therefore do not intersect.
• The system has no solution.

Would you like more details on how to identify inconsistent systems or how parallel lines behave algebraically?

Here are 5 related questions:

1. How do you recognize when two lines are parallel from their equations?
2. What are the conditions under which two lines are parallel in a system of linear equations?
3. How do you interpret $0 = 0$ in a system of equations?
4. What are the differences between inconsistent and dependent systems?
5. How do you graphically solve a system of equations?

Tip: When solving systems using substitution or elimination, if you reach a contradiction like $0 = 4$, it’s an immediate indicator that the system has no solution and the lines are parallel.