We are given the system of equations:

-2x + y = 6 \tag{1} x - y = 1 \tag{2}

We can solve this system by substitution or elimination. Let's use substitution for simplicity.

From equation (2), solve for $y$ in terms of $x$: x - y = 1 \quad \Rightarrow \quad y = x - 1 \tag{3}

Now substitute $y = x - 1$ from equation (3) into equation (1): $-2x + (x - 1) = 6$

Simplify and solve for $x$: $-2x + x - 1 = 6$ $-x - 1 = 6$ $-x = 7$ $x = -7$

So the value of $x$ is $-7$.

The correct answer is B. -7.

Would you like more details or further explanation?

Here are five related questions for practice:

1. What is the value of $y$ in the solution to this system?
2. How would you solve the system using the elimination method?
3. Can a system of equations have no solutions? If so, how can you tell?
4. How would you solve a system of equations graphically?
5. What happens if both equations represent the same line?

Tip: Always check your solution by substituting the values of $x$ and $y$ back into both original equations.