To solve the system of equations:

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

We can solve this system by substitution or elimination. Here, we'll use substitution.

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

From Equation (2), solve for $y$: $x - y = 1 \implies y = x - 1 \quad \text{(3)}$

Step 2: Substitute Equation (3) into Equation (1)

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: $x = -7$

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

The correct answer is B. -7.

Would you like more details or have any questions?

Here are some related questions you might explore:

1. What is the value of $y$ in this system?
2. How would you solve this system using the elimination method?
3. What happens if both equations are multiplied by a constant before solving?
4. How can you check if your solution is correct?
5. What does the graph of these two equations look like?

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