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To solve this system of equations by eliminating one of the variables, we need to examine the coefficients of \( x \) and \( y \) in each equation:

\[
-6x + 7y = -54
\]
\[
-7x + 7y = -56
\]

1. Notice that both equations have \( 7y \) as the \( y \)-coefficient. This means that if we subtract one equation from the other, we can eliminate \( y \), because \( 7y - 7y = 0 \).

2. Subtracting the second equation from the first (or vice versa) will result in an equation with only \( x \), allowing us to solve for \( x \) first.

Thus, the correct first step is:
- **Subtract to eliminate \( y \)**.

Would you like a detailed solution of the entire system? 

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Here are some additional questions for further exploration:

1. What would happen if we chose to add the equations instead of subtracting?
2. Can this system be solved by elimination of \( x \) instead?
3. What are other methods to solve systems of equations, apart from elimination?
4. Why does the elimination method work effectively in this system?
5. How can we verify the solution after solving?

**Tip:** When both equations have the same coefficient for one variable, subtracting them is often an effective way to eliminate that variable.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step:

-6x + 7y = -54
-7x + 7y = -56

Answer choices:
- Add to eliminate y.
- Subtract to eliminate x.
- Subtract to eliminate y.
- Add to eliminate x.

Learn how to solve a system of linear equations by eliminating variables. In this problem, we examine whether to add or subtract equations to eliminate x or y. This guide is ideal for students in Grades 8-10, covering core algebraic techniques.

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