To solve the system of equations:

1. $-2x + y = 6$
2. $x - y = 1$

We can use substitution or elimination. Let's solve this using substitution.

Step 1: Solve the second equation for $y$

From the second equation $x - y = 1$, solve for $y$: $y = x - 1$

Step 2: Substitute $y = x - 1$ into the first equation

Substitute this into the first equation $-2x + y = 6$: $-2x + (x - 1) = 6$ Now simplify and solve for $x$: $-2x + x - 1 = 6$ $-x - 1 = 6$ $-x = 7$ $x = -7$

Thus, the value of $x$ is $\boxed{-7}$.

The correct answer is B. -7.

Would you like to see a detailed breakdown of the steps or have any questions?

Here are some related questions:

1. How would you solve this system using the elimination method?
2. How would you check your solution to ensure it's correct?
3. What are some common methods to solve systems of equations?
4. How does substitution differ from elimination in solving systems?
5. What happens if both equations are dependent (i.e., multiples of each other)?

Tip: Always substitute your value back into both original equations to confirm your solution is correct!