https://file.aiquickdraw.com/mathbot/file/1727187140554xuuhyx56.jpg

The system of equations given in the image is:

\[
\begin{cases}
-5x - 2y = -8 \\
x - 2y = 4
\end{cases}
\]

We can solve this system using substitution or elimination. I'll use the substitution method.

### Step 1: Solve for \(x\) from the second equation.
From the second equation:

\[
x - 2y = 4 \implies x = 4 + 2y
\]

### Step 2: Substitute this expression for \(x\) into the first equation.

\[
-5(4 + 2y) - 2y = -8
\]

Simplify:

\[
-20 - 10y - 2y = -8 \implies -20 - 12y = -8
\]

### Step 3: Solve for \(y\).

\[
-12y = -8 + 20 \implies -12y = 12 \implies y = -1
\]

### Step 4: Substitute \(y = -1\) back into the expression for \(x\).

\[
x = 4 + 2(-1) = 4 - 2 = 2
\]

Thus, the solution is \(x = 2\) and \(y = -1\), which corresponds to the point \((2, -1)\).

### Answer:
The correct choice is **(b) (2, -1)**.

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Would you like further details on this method or clarification on a specific part? Here are five related questions you could explore:

1. How does the elimination method work for solving systems of equations?
2. Can you solve this system using matrix methods like Gaussian elimination?
3. What are the conditions for a system of equations to have no solution or infinite solutions?
4. How can we graphically interpret the solution to this system of equations?
5. How do linear systems behave when one equation is a multiple of the other?

**Tip:** Always double-check your substitution steps to avoid small errors that can lead to incorrect solutions.

Solve the system of equations: -5x - 2y = -8 and x - 2y = 4. Which of the following is the solution? (a) (-1, 2), (b) (2, -1), (c) (1, -2), (d) (-2, 1).

Learn how to solve a system of linear equations using the substitution method. This detailed solution walks through solving -5x - 2y = -8 and x - 2y = 4, guiding students to the correct solution (2, -1). Suitable for students in Grades 8-10.

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