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We have the following system of linear equations:

1) \( x - 8y = -24 \)
2) \( 5x + 8y = -24 \)

To solve this system, we can add the two equations together to eliminate \(y\). Let's proceed step by step:

### Step 1: Add the two equations
\[
(x - 8y) + (5x + 8y) = -24 + (-24)
\]
\[
x + 5x = -48
\]
\[
6x = -48
\]

### Step 2: Solve for \(x\)
\[
x = \frac{-48}{6} = -8
\]

### Step 3: Substitute \(x = -8\) into one of the original equations (I'll use the first equation):
\[
x - 8y = -24
\]
Substitute \(x = -8\):
\[
-8 - 8y = -24
\]
\[
-8y = -24 + 8
\]
\[
-8y = -16
\]

### Step 4: Solve for \(y\)
\[
y = \frac{-16}{-8} = 2
\]

### Final Answer:
The solution is \( x = -8 \) and \( y = 2 \).

Would you like further details or clarification on any of these steps?

Here are five questions that build on this concept:
1. How would the solution change if the coefficients of \( y \) in both equations were different?
2. What other methods can be used to solve systems of equations, besides elimination?
3. How can we check if the solution \( x = -8 \) and \( y = 2 \) is correct?
4. What happens if the system of equations has no solutions or infinitely many solutions?
5. How can you solve a system of equations graphically?

**Tip:** When solving a system of linear equations, always verify the solution by substituting the values back into the original equations.

Solve the system of linear equations: 1) x - 8y = -24 and 2) 5x + 8y = -24.

Learn how to solve a system of linear equations using the elimination method. This detailed solution involves the equations x - 8y = -24 and 5x + 8y = -24. Suitable for students in Grades 8-10. Understand key algebraic concepts and theorems step-by-step.

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