https://file.aiquickdraw.com/mathbot/file/1729194524163f3gj47if.jpg

The system of equations provided in the image is:

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

We need to solve for the value of \(x\). 

### Step 1: Solve one equation for \(y\)
From the second equation, solve for \(y\):
\[
x - y = 1 \implies y = x - 1
\]

### Step 2: Substitute into the first equation
Now substitute \(y = x - 1\) into the first equation:
\[
-2x + (x - 1) = 6
\]
Simplify:
\[
-2x + x - 1 = 6 \implies -x - 1 = 6
\]
Add 1 to both sides:
\[
-x = 7 \implies x = -7
\]

Thus, the value of \(x\) is \(\boxed{-7}\).

Would you like more details or have any questions about this process? 

### Here are 5 related questions:
1. How do you solve systems of equations using substitution?
2. How would you solve this system using the elimination method?
3. What happens if both equations had the same slope?
4. Can systems of equations have no solution or infinitely many solutions?
5. How can we graphically interpret the solution to this system?

### Tip: Always check your solution by substituting both values of \(x\) and \(y\) back into the original equations!

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

Learn how to solve a system of equations using the substitution method with the example: -2x + y = 6 and x - y = 1. This algebra problem is suitable for students in Grades 8-10.

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