To find the intersection of the lines:

1. $2x + 3y = 5$
2. $2x + 3y = 10$

We compare these two equations. Notice that the left-hand sides are identical ($2x + 3y$), but the right-hand sides are different ($5$ and $10$).

Analysis:

If we subtract the first equation from the second, we get: $(2x + 3y) - (2x + 3y) = 10 - 5$ $0 = 5$

This is a contradiction. It means that the two lines are parallel and do not intersect.

Conclusion:

The two lines have no point of intersection because they are parallel.

Would you like me to explain this further or provide a graphical representation? Let me know!

Here are 5 related questions to deepen your understanding:

1. What is the geometric meaning of parallel lines?
2. How can we determine if two lines are parallel using their slopes?
3. What happens if the two equations represent the same line instead of distinct ones?
4. How can we find the intersection of lines that are not parallel?
5. How can systems of equations like this be solved using substitution or elimination?

Tip: When two linear equations have the same left-hand side but different right-hand sides, the lines are always parallel!