The equation $3 = 2$ is a contradiction, meaning that the system of equations has no solution. This happens when the two equations in the system represent parallel lines.

What is true about the slopes and y-intercepts?

• Slopes: The slopes of the lines are the same. This is because parallel lines have identical slopes.
• Y-intercepts: The y-intercepts of the lines are different. This difference is what ensures that the lines never intersect, creating a system with no solution.

Would you like me to go deeper into solving such systems or explaining parallel lines in detail?

Here are 5 questions to expand on this:

1. How can we determine whether two lines are parallel from their equations?
2. What happens if the slopes are the same but the y-intercepts are also the same?
3. Can you provide an example of a system of equations that would result in a contradiction like $3 = 2$?
4. How does substitution help identify inconsistent systems?
5. What are the geometric interpretations of consistent, inconsistent, and dependent systems?

Tip: To spot parallel lines in slope-intercept form ($y = mx + b$), compare their slopes ($m$)—if they are equal and their y-intercepts ($b$) are different, the lines are parallel.