We are given the following system of equations:

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

To find the value of $x$, let's solve the system step by step.

Step 1: Solve for $y$ in the second equation

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

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

Now, substitute this expression for $y$ into the first equation: $-2x + (x - 1) = 6$

Step 3: Simplify and solve for $x$

Simplify the equation: $-2x + x - 1 = 6$ $-x - 1 = 6$ Add 1 to both sides: $-x = 7$ Now, multiply by $-1$ to isolate $x$: $x = -7$

Thus, the value of $x$ is $-7$.

Answer:

The correct answer is $\boxed{-7}$, which corresponds to option B.

Would you like a more detailed explanation of any part of the process?

Here are five related questions to practice:

1. What is the value of $y$ in the solution to this system of equations?
2. How can you check that your solution for $x$ and $y$ is correct?
3. How would the solution change if the second equation were $x + y = 1$ instead of $x - y = 1$?
4. What are the advantages of using substitution over elimination in solving this system?
5. How do you graphically represent the solution to this system of equations?

Tip: Always substitute your solution back into the original equations to verify its correctness.