We are given the system of equations:

$-2x + y = 6 \quad \text{(1)}$ $x - y = 1 \quad \text{(2)}$

To find the value of $x$, we can solve this system using substitution or elimination. Here, we'll use the substitution method.

Step 1: Solve equation (2) for $y$

From equation (2): $x - y = 1$ Solve for $y$: $y = x - 1$

Step 2: Substitute $y = x - 1$ into equation (1)

Now, substitute $y = x - 1$ into equation (1): $-2x + (x - 1) = 6$ Simplify the equation: $-2x + x - 1 = 6$ $-x - 1 = 6$ Add 1 to both sides: $-x = 7$ Multiply both sides by $-1$: $x = -7$

Final Answer:

The value of $x$ is $\boxed{-7}$.

The correct answer is B.‒7.

Would you like a detailed explanation of any step?

Here are some related questions:

1. How would the elimination method work for this system of equations?
2. How can you check your solution after finding $x$ and $y$?
3. What are the properties of a system of linear equations like this one?
4. What happens if the system of equations has no solution or infinite solutions?
5. How do systems of equations relate to real-world problems?

Tip: When solving systems of equations, substitution is often helpful when one variable is already isolated or easy to isolate.