https://file.aiquickdraw.com/mathbot/file/17266752329483l2k0gz1.jpg

The system of equations provided is:

\[
\begin{aligned}
1. & \quad 8x + y = -13 \\
2. & \quad -8x - 2y = 10
\end{aligned}
\]

### Step-by-Step Solution:

#### Step 1: Add the two equations together
Notice that adding the two equations will allow us to eliminate \(x\), since the coefficients of \(x\) are opposite (8 and -8).

\[
(8x + y) + (-8x - 2y) = -13 + 10
\]
This simplifies to:
\[
0x - y = -3
\]
\[
-y = -3 \quad \text{so} \quad y = 3
\]

#### Step 2: Substitute \(y = 3\) into one of the original equations
We can substitute \(y = 3\) into the first equation to solve for \(x\):

\[
8x + 3 = -13
\]
Subtract 3 from both sides:
\[
8x = -16
\]
Now, divide by 8:
\[
x = -2
\]

### Final Solution:
The solution to the system of equations is:
\[
x = -2, \quad y = 3
\]

Would you like further details or have any questions about this process? 

Here are 5 related questions:
1. What is the substitution method for solving systems of equations?
2. How do you solve systems of equations using matrices?
3. What are the conditions for a system of equations to have no solution?
4. How can graphing be used to solve systems of equations?
5. How do you solve a system of equations with three variables?

**Tip:** Always check your solution by substituting the values back into the original equations!

Find the solution of the system of equations: 8x + y = -13 and -8x - 2y = 10.

Learn how to solve the system of linear equations: 8x + y = -13 and -8x - 2y = 10 using the elimination and substitution methods. This solution is suitable for students in Grades 8-10 and covers essential algebra concepts.

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