Adria has the following system of equations on her math homework.
 
‒2x+y=6
x−y=1

What is the value of x
 in the solution to this system of equations?
A.7

B.‒7

C.8

D.‒8


We are given the system of equations:

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

To find the value of \( x \), we can solve this system using substitution or elimination. Here, we'll use the substitution method.

### Step 1: Solve equation (2) for \( y \)

From equation (2):
\[
x - y = 1
\]
Solve for \( y \):
\[
y = x - 1
\]

### Step 2: Substitute \( y = x - 1 \) into equation (1)

Now, 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 \(-1\):
\[
x = -7
\]

### Final Answer:
The value of \( x \) is \( \boxed{-7} \).

The correct answer is **B.‒7**.

Would you like a detailed explanation of any step? 

Here are some related questions:
1. How would the elimination method work for this system of equations?
2. How can you check your solution after finding \( x \) and \( y \)?
3. What are the properties of a system of linear equations like this one?
4. What happens if the system of equations has no solution or infinite solutions?
5. How do systems of equations relate to real-world problems?

**Tip:** When solving systems of equations, substitution is often helpful when one variable is already isolated or easy to isolate.

Adria has the following system of equations on her math homework: -2x + y = 6, x - y = 1. What is the value of x in the solution to this system of equations? A. 7, B. ‒7, C. 8, D. ‒8

Learn how to solve the system of linear equations -2x + y = 6 and x - y = 1 using the substitution method. This problem covers key algebraic concepts and is suitable for students in Grades 8-10. The solution leads to finding x = ‒7, and is presented step by step.

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