https://file.aiquickdraw.com/mathbot/file/1726063373239l1h1fij5.jpg

The system of linear equations shown in the image is:

\[
\text{1. } 2x - 4y = 6
\]
\[
\text{2. } -x + 2y = 7
\]

I will now solve this system of equations using either substitution or elimination method. Let's proceed with the elimination method since it looks more straightforward here.

We can multiply the second equation by 2 so that the \( x \) terms cancel out:

\[
-2x + 4y = 14
\]

Now we add the two equations:

\[
(2x - 4y) + (-2x + 4y) = 6 + 14
\]
\[
0 = 20
\]

This results in an inconsistent equation, indicating that there is no solution to this system of equations. Therefore, the system is inconsistent, meaning that the two lines represented by these equations are parallel and do not intersect.

Would you like more details on this, or do you have any other questions? 

Here are some related questions to explore:

1. What does it mean for a system of equations to be inconsistent?
2. How can you determine if two lines are parallel using their slopes?
3. Can a system of linear equations have infinitely many solutions?
4. What is the graphical interpretation of solving two equations simultaneously?
5. How does the elimination method work for solving systems of linear equations?

**Tip:** When solving systems of equations, try to recognize early on if multiplying the equations leads to cancellation or an inconsistent result, as this saves time when identifying parallel lines or no solutions.

Learn how to solve a system of linear equations using the elimination method. In this problem, the system of equations is 2x - 4y = 6 and -x + 2y = 7. The solution demonstrates the inconsistency of the system, leading to the conclusion that the lines are parallel and have no solution.

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