To solve the system of equations:

1. **First equation:**  
   \(2x - y = 7\)  
   Rearranging for \(y\):  
   \(y = 2x - 7\)

2. **Second equation:**  
   \(6x - 3y = 14\)  
   This can be simplified by dividing all terms by 3:  
   \(2x - y = \frac{14}{3}\)

Now, we have the two equations:  
- \(y = 2x - 7\)  
- \(2x - y = \frac{14}{3}\)

Substituting \(y\) from the first equation into the second:

\[
2x - (2x - 7) = \frac{14}{3}
\]
\[
7 = \frac{14}{3}
\]

This is a contradiction, indicating that the two lines represented by these equations are parallel and do not intersect. Thus, there is no solution.

### Summary
The system has no solution, meaning the lines are parallel.

Would you like more details on any part of this solution, or do you have other questions? Here are some related questions you might consider:

1. What does it mean for two lines to be parallel in terms of their equations?
2. How can you graph these equations to visualize their relationship?
3. What are alternative methods to solve systems of equations?
4. Can you provide an example of a system of equations with a unique solution?
5. What would change if the second equation was \(6x - 3y = 21\)?

**Tip:** When solving systems of equations, always check for inconsistencies to determine if solutions exist.

Discover how to solve the system of equations 2x − y = 7 and 6x − 3y = 14, revealing that there is no solution as the lines are parallel. This solution involves key algebraic concepts and properties of linear equations, ideal for students in Grades 8-10.

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