To solve the system of equations given by:

1. \( y = -4x + 7 \)
2. \( 8x + 2y = -4 \)

we can substitute the expression for \( y \) from the first equation into the second equation.

### Step 1: Substitute \( y \)

Substituting \( y \) into the second equation:

\[
8x + 2(-4x + 7) = -4
\]

### Step 2: Simplify the equation

Distributing \( 2 \):

\[
8x - 8x + 14 = -4
\]

This simplifies to:

\[
14 = -4
\]

### Conclusion

Since \( 14 \neq -4 \), this indicates that the system of equations is inconsistent, meaning there are no solutions. The lines represented by these equations are parallel.

### Further Considerations

If you have any specific questions or need more details about the solution process, feel free to ask! Here are some follow-up questions:

1. Would you like to see the graphical representation of these equations?
2. Do you want to learn about methods for solving systems of equations?
3. Are you interested in understanding parallel lines in more detail?
4. Would you like to explore how to derive equations from a given graph?
5. Is there another system of equations you would like to solve?

**Tip:** Always check if the coefficients allow for a unique solution, no solution, or infinitely many solutions by examining the relationships between the equations.

Discover how to solve the system of equations y = -4x + 7 and 8x + 2y = -4 with a comprehensive step-by-step guide. This solution highlights key algebraic concepts, including the substitution method and the condition for parallel lines, suitable for students in Grades 8-10.

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