https://file.aiquickdraw.com/mathbot/file/1734363206033bpn9tecp.jpg

To solve the given system of equations:

\[
\begin{cases}
-8x + 4y = -2 \\
4x - 2y = 1
\end{cases}
\]

### Step 1: Simplify the equations
Both equations have common factors. Let's simplify each equation:
1. Divide the first equation by \( -2 \):
   \[
   -8x + 4y = -2 \quad \Rightarrow \quad 4x - 2y = 1
   \]
2. The second equation is already \( 4x - 2y = 1 \).

### Step 2: Analyze the simplified system
After simplifying, the system becomes:
\[
\begin{cases}
4x - 2y = 1 \\
4x - 2y = 1
\end{cases}
\]

Both equations are identical, which means they represent the same line.

### Step 3: Determine the solution
Since the two equations are the same, there are **infinitely many solutions**. Any point on the line \( 4x - 2y = 1 \) satisfies the system.

### Final Answer:
\[
\text{inf.}
\]

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Do you want further details or examples on solving systems of equations? Let me know!

### Related Questions:
1. How do you solve a system of equations using substitution?
2. What is the elimination method for solving systems of equations?
3. How do you identify no solutions or infinitely many solutions graphically?
4. Solve a system with different coefficients but no solutions.
5. What is a consistent and dependent system of linear equations?

**Tip:** For systems with identical equations, the solution set is infinite and can be described using one of the variables (e.g., \( y \) in terms of \( x \)).

What is the solution to the system of equations {-8x + 4y = -2, 4x - 2y = 1}?

Learn how to determine the solution to the system of equations {-8x + 4y = -2, 4x - 2y = 1}. This problem simplifies to a dependent system, resulting in infinitely many solutions. Suitable for students in Grades 8-10 studying systems of equations.

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