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We are given the following system of equations to solve for \( x \):

\[
\begin{aligned}
-2x + y &= 6 \\
x - y &= 1
\end{aligned}
\]

### Step 1: Solve one equation for one variable.
We can solve the second equation for \( y \):

\[
x - y = 1 \quad \Rightarrow \quad y = x - 1
\]

### Step 2: Substitute the expression for \( y \) into the first equation.
Substitute \( y = x - 1 \) into the first equation:

\[
-2x + (x - 1) = 6
\]

Simplify the equation:

\[
-2x + x - 1 = 6 \quad \Rightarrow \quad -x - 1 = 6
\]

### Step 3: Solve for \( x \).
Now, solve for \( x \):

\[
-x = 6 + 1 \quad \Rightarrow \quad -x = 7 \quad \Rightarrow \quad x = -7
\]

So, the value of \( x \) is \( -7 \).

The correct answer is **B. -7**.

Would you like more details or have any questions?

Here are five related questions to expand on this:

1. How do you solve a system of equations using the substitution method?
2. How can you check if the solution to a system of equations is correct?
3. What are the different methods to solve a system of linear equations?
4. What happens if both equations in a system are multiples of each other?
5. Can a system of equations have no solution or infinite solutions? How would you recognize it?

**Tip**: Always substitute your found values back into the original equations to verify your solution!

What is the value of x in the solution to the system of equations?
-2x + y = 6
x - y = 1

Learn how to solve the system of linear equations -2x + y = 6 and x - y = 1 using the substitution method. This step-by-step guide covers key algebraic concepts for students in Grades 8-10.

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