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:

\[
-2x + y = 6 \tag{1}
\]
\[
x - y = 1 \tag{2}
\]

We can solve this system by substitution or elimination. Let's use substitution for simplicity.

From equation (2), solve for \( y \) in terms of \( x \):
\[
x - y = 1 \quad \Rightarrow \quad y = x - 1 \tag{3}
\]

Now substitute \( y = x - 1 \) from equation (3) into equation (1):
\[
-2x + (x - 1) = 6
\]

Simplify and solve for \( x \):
\[
-2x + x - 1 = 6
\]
\[
-x - 1 = 6
\]
\[
-x = 7
\]
\[
x = -7
\]

So the value of \( x \) is \( -7 \).

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

Would you like more details or further explanation?

Here are five related questions for practice:
1. What is the value of \( y \) in the solution to this system?
2. How would you solve the system using the elimination method?
3. Can a system of equations have no solutions? If so, how can you tell?
4. How would you solve a system of equations graphically?
5. What happens if both equations represent the same line?

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

Learn how to solve a system of linear equations using substitution and elimination methods. This problem involves solving the equations ‒2x + y = 6 and x − y = 1 to find the value of x. Step-by-step solution included. Suitable for students in Grades 8-10.

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