The system of equations you provided is:

1. \( x + 2y = 10 \)
2. \( x + 2y = 8 \)

Now, let's analyze these equations. Subtract the second equation from the first:

\[
(x + 2y) - (x + 2y) = 10 - 8
\]

This simplifies to:

\[
0 = 2
\]

This is a contradiction, which means there is no solution to this system of equations. The two lines represented by these equations are parallel and do not intersect.

Would you like more details or have any questions?

Here are 5 related questions:
1. How can we identify parallel lines from a system of equations?
2. What are the methods to solve systems of equations?
3. Can two parallel lines ever have a solution in a system of equations?
4. What is the difference between inconsistent, consistent, and dependent systems of equations?
5. How would graphing these two equations show that they are parallel?

**Tip:** Inconsistent systems have no solution because the lines never intersect!

This page provides a step-by-step solution to the system of equations x + 2y = 10 and x + 2y = 8, demonstrating why the system is inconsistent. Learn about parallel lines and the concept of inconsistent systems, suitable for students in Grades 8-10.

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