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 can solve this system of equations using substitution or elimination. Let's use substitution to find the value of \( x \).

The system of equations is:
1. \(-2x + y = 6\)
2. \(x - y = 1\)

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

### Step 2: Substitute \( y = x - 1 \) into the first equation:
Substitute this into the first equation:
\[
-2x + (x - 1) = 6
\]
Simplify the equation:
\[
-2x + x - 1 = 6
\]
\[
-x - 1 = 6
\]
### Step 3: Solve for \( x \):
Add 1 to both sides:
\[
-x = 7
\]
Multiply both sides by -1:
\[
x = -7
\]

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

Would you like more details on this method? Here are some related questions:

1. How can we solve the system using the elimination method?
2. What is the value of \( y \) in this system?
3. How can systems of equations be used in real-world scenarios?
4. What are some other methods for solving systems of equations?
5. What happens when a system has no solutions or infinitely many solutions?

**Tip:** Always check your solution by substituting the values 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

Learn how to solve the system of linear equations ‒2x + y = 6 and x − y = 1 using the substitution method. This detailed step-by-step solution covers important algebraic concepts and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation