https://file.aiquickdraw.com/mathbot/file/1726707357364x4wdo3rf.jpg

The system of equations shown in the image is:

\[
\text{System A:}
\begin{cases}
-5x - y = -5 \\
-5x + y = -5
\end{cases}
\]

We can solve this system using the elimination method. 

1. Add the two equations to eliminate \(y\):

\[
(-5x - y) + (-5x + y) = -5 + (-5)
\]

This simplifies to:

\[
-10x = -10
\]

Solving for \(x\):

\[
x = \frac{-10}{-10} = 1
\]

2. Substitute \(x = 1\) into either of the original equations (I'll use the first equation):

\[
-5(1) - y = -5
\]

\[
-5 - y = -5
\]

Add 5 to both sides:

\[
-y = 0
\]

So:

\[
y = 0
\]

The solution to the system is:

\[
x = 1, \quad y = 0
\]

Would you like more details or explanations?

Here are 5 related questions to deepen your understanding:
1. How would the solution change if the signs in the equations were reversed?
2. Can you solve the system by substitution instead of elimination?
3. What happens if we graph the two equations? What does their intersection point represent?
4. How can you check if the solution \((1, 0)\) is correct by substituting back into both equations?
5. How does solving a system with no solutions differ from solving this system?

**Tip:** Always verify your solution by substituting the values of \(x\) and \(y\) back into the original equations to ensure both are satisfied.

Solve the system of equations: -5x - y = -5 and -5x + y = -5.

Learn how to solve the system of linear equations -5x - y = -5 and -5x + y = -5 using the elimination method. This problem involves key algebraic concepts, such as eliminating variables and solving for x and y, suitable for students in Grades 9-10.

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