https://file.aiquickdraw.com/mathbot/file/1729777285098m188tqmq.jpg

The system of equations extracted from the image is:

\[
\begin{cases} 
-8x + 4y = 24 \\
-7x + 7y = 28
\end{cases}
\]

Now, solving for \( x \) and \( y \):

1. From the second equation \( -7x + 7y = 28 \), divide by 7:
   \[
   -x + y = 4 \quad \Rightarrow \quad y = x + 4
   \]

2. Substitute \( y = x + 4 \) into the first equation:
   \[
   -8x + 4(x + 4) = 24
   \]
   Expanding and solving for \( x \):
   \[
   -8x + 4x + 16 = 24 \quad \Rightarrow \quad -4x + 16 = 24 \quad \Rightarrow \quad -4x = 8 \quad \Rightarrow \quad x = -2
   \]

3. Substitute \( x = -2 \) into \( y = x + 4 \):
   \[
   y = -2 + 4 = 2
   \]

Thus, the solution is \( x = -2 \) and \( y = 2 \).

Let me know if you'd like further details or have any questions.

Here are five related questions to further explore:
1. How would you solve the system graphically?
2. What are some methods to verify the solution?
3. Can this system be solved using matrices?
4. What happens if we solve using substitution versus elimination?
5. How would a small change in the coefficients affect the solution?

**Tip:** Always verify the solution by substituting the values back into the original equations to ensure accuracy.

Solve the system of equations: -8x + 4y = 24 and -7x + 7y = 28

Learn how to solve the linear system of equations: -8x + 4y = 24 and -7x + 7y = 28. This step-by-step guide uses the substitution method, covering key algebra concepts. Suitable for students in Grades 8-10.

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