Let's solve the given system of equations:

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

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

1. Solve the second equation for $y$: $y = x - 1$

2. Substitute $y = x - 1$ into the first equation: $-2x + (x - 1) = 6$ Simplify this: $-2x + x - 1 = 6$ $-x - 1 = 6$

3. Solve for $x$: $-x = 6 + 1$ $-x = 7$ $x = -7$

So, the solution for $x$ is $\boxed{-7}$. The correct answer is B. -7.

Would you like more details on how this was solved, or do you have any questions?

Here are 5 related questions:

1. How can the elimination method be used to solve this system?
2. What is the value of $y$ in the solution?
3. How can you graphically represent this system of equations?
4. What is a consistent and independent system of equations?
5. How does substitution work for solving systems of equations with more variables?

Tip: Always check your solution by substituting back into the original equations to verify accuracy.