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


Let's solve the system of equations step by step to find the value of \( x \).

The system of equations is:
\[
-2x + y = 6 \tag{1}
\]
\[
x - y = 1 \tag{2}
\]

### Step 1: Solve Equation (2) for \( y \)
From Equation (2), we can express \( y \) in terms of \( x \):
\[
x - y = 1 \quad \Rightarrow \quad y = x - 1
\]

### Step 2: Substitute \( y = x - 1 \) into Equation (1)
Now, substitute \( y = x - 1 \) into Equation (1):
\[
-2x + (x - 1) = 6
\]
Simplify the equation:
\[
-2x + x - 1 = 6
\]
\[
-x - 1 = 6
\]
\[
-x = 7
\]
\[
x = -7
\]

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

The correct answer is:
\[
\text{B.} -7
\]

Would you like to go over any specific part of the solution or have any further questions?

Here are some related questions to explore:
1. How do we solve a system of equations using substitution?
2. What happens if we solve the system using the elimination method instead?
3. Can all systems of linear equations be solved using substitution?
4. What is the difference between consistent and inconsistent systems?
5. How can graphing help in solving systems of linear equations?

**Tip:** Substitution works best when one equation is already solved for one variable, making it easier to substitute into the other equation.

Adria has the following system of equations on her math homework. ‒2x + y = 6 and 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 equations ‒2x + y = 6 and x − y = 1 using the substitution method. This detailed step-by-step solution explains key algebraic concepts for students in Grades 8-10. Discover how to simplify and solve for x in a system of linear equations.

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