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


To solve the system of equations:

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

We can solve this system by substitution or elimination. Here, we'll use substitution.

### Step 1: Solve Equation (2) for \( y \)
From Equation (2), solve for \( y \):
\[
x - y = 1 \implies y = x - 1 \quad \text{(3)}
\]

### Step 2: Substitute Equation (3) into Equation (1)
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:
\[
x = -7
\]

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

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

Would you like more details or have any questions?

Here are some related questions you might explore:
1. What is the value of \( y \) in this system?
2. How would you solve this system using the elimination method?
3. What happens if both equations are multiplied by a constant before solving?
4. How can you check if your solution is correct?
5. What does the graph of these two equations look like?

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

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

Find the value of x in the system of linear equations -2x + y = 6 and x - y = 1. This step-by-step solution uses the substitution method to solve the system, ideal for students in Grades 7-9 learning algebraic concepts such as solving systems of equations.

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