https://file.aiquickdraw.com/mathbot/file/1736243652764aqs7ai7y.jpg

The system of equations provided is:

\[
\begin{aligned}
\text{1. } & 2x + y = 8 \quad (\text{Eq. 1}) \\
\text{2. } & 2x + y = 4 \quad (\text{Eq. 2})
\end{aligned}
\]

### Step 1: Compare the two equations
Notice that both equations have the same left-hand side (\(2x + y\)), but their right-hand sides differ (\(8 \neq 4\)).

### Step 2: Subtract Eq. 2 from Eq. 1
\[
(2x + y) - (2x + y) = 8 - 4
\]
\[
0 = 4
\]

This is a **contradiction**, meaning the system of equations has no solution. 

### Final Conclusion:
The system is **inconsistent**, and the equations represent parallel lines that never intersect.

Would you like more details or have any other questions? 😊  

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### 5 Related Questions:
1. How do we determine if a system of equations is inconsistent?
2. Can you show the graph of these two equations?
3. What happens if two equations have the same slope but different intercepts?
4. What does it mean when a system of equations has infinitely many solutions?
5. How can we rewrite inconsistent systems into matrix form?

### Tip:
Always check if the equations are multiples of each other when comparing them—it can quickly reveal inconsistencies or redundancies!

Solve the system of equations: 2x + y = 8 and 2x + y = 4.

Learn how to solve the system of equations 2x + y = 8 and 2x + y = 4. This problem explores inconsistent systems of equations, including parallel lines and algebraic contradictions. Suitable for Grades 8-10.

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