https://file.aiquickdraw.com/mathbot/file/1728140973630omgsl1g7.jpg

The system of equations in the image is:

1. \( 8x - y = -4 \)
2. \( 4x + 7y = -32 \)

Both substitution and elimination methods would work here, but elimination may be more efficient given the structure of the equations. Let's use elimination to solve this.

### Elimination Method:

Step 1: Multiply both sides of the first equation by 7 to eliminate \( y \) when we add the two equations together.

\[
7(8x - y) = 7(-4)
\]
\[
56x - 7y = -28
\]

So now, we have the following system:

1. \( 56x - 7y = -28 \)
2. \( 4x + 7y = -32 \)

Step 2: Add the two equations together to eliminate \( y \).

\[
(56x - 7y) + (4x + 7y) = (-28) + (-32)
\]
\[
60x = -60
\]

Step 3: Solve for \( x \).

\[
x = \frac{-60}{60} = -1
\]

Step 4: Substitute \( x = -1 \) into the first equation to solve for \( y \).

\[
8(-1) - y = -4
\]
\[
-8 - y = -4
\]
\[
-y = -4 + 8
\]
\[
-y = 4 \quad \Rightarrow \quad y = -4
\]

### Solution:
The solution to the system of equations is:
\[
x = -1, \quad y = -4
\]

Would you like further clarification on any step or more details?

Here are some related questions:
1. What is the substitution method and how does it differ from elimination?
2. Can the substitution method also solve this system of equations?
3. How do you check if a solution is correct for a system of equations?
4. Why might elimination be more efficient in some cases than substitution?
5. Can systems of equations sometimes have no solutions or infinitely many solutions?

**Tip:** When using elimination, it's useful to multiply the equations in a way that cancels out one of the variables immediately.

Would you use substitution or elimination to solve the system of equations: 8x - y = -4 and 4x + 7y = -32?

Learn how to solve the system of equations 8x - y = -4 and 4x + 7y = -32 using the elimination method. This step-by-step guide covers essential algebraic concepts, perfect for students in Grades 8-10.

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