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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.

What is the value of x in the solution to this 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. Detailed step-by-step explanation. Ideal for students in Grades 8-10.

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