Solve the system by the addition method.

2x+2y=6

2x−2y=6


**A.**The solution is enter your response here. ​(Type an ordered​ pair.)

**B.**There are infinitely many solutions.

**C.**There is no solution. 

To solve the system by the addition method, follow these steps:

### Step 1: Write down the system of equations.
\[
\text{1. } 2x + 2y = 6
\]
\[
\text{2. } 2x - 2y = 6
\]

### Step 2: Add the equations to eliminate one variable.
We add the two equations together:
\[
(2x + 2y) + (2x - 2y) = 6 + 6
\]
This simplifies to:
\[
4x = 12
\]

### Step 3: Solve for \(x\).
\[
x = \frac{12}{4} = 3
\]

### Step 4: Substitute \(x = 3\) into one of the original equations to solve for \(y\).
Substitute \(x = 3\) into the first equation:
\[
2(3) + 2y = 6
\]
This simplifies to:
\[
6 + 2y = 6
\]
\[
2y = 0
\]
\[
y = 0
\]

### Final Answer:
The solution is \( (3, 0) \).

**A.** The solution is \((3, 0)\).

Would you like further clarification?

---

Here are 5 related questions:
1. How does the addition method differ from substitution in solving systems of equations?
2. What happens if both variables cancel out when using the addition method?
3. How can you tell if a system has no solution or infinitely many solutions?
4. What does it mean when a system of equations is inconsistent?
5. Can you solve a system with three variables using the addition method?

**Tip:** Always check your solution by substituting the values back into the original equations to verify.

Solve the system by the addition method.

2x + 2y = 6

2x - 2y = 6

**A.** The solution is enter your response here. (Type an ordered pair.)

**B.** There are infinitely many solutions.

**C.** There is no solution.

Learn how to solve a system of linear equations using the addition method. This example solves 2x + 2y = 6 and 2x - 2y = 6 step by step, explaining how to eliminate variables and find the solution (3, 0). Perfect for Grades 8-10 algebra students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation