Solve the system of equations by the addition method.

5 x plus y5x+y

equals=

1212

6 x minus y6x−y

equals=

1010

To solve the system of equations using the addition method, we first write out the equations clearly:

1. \( 5x + y = 12 \)
2. \( 6x - y = 10 \)

### Step-by-step solution:

1. **Add the two equations**:  
   We do this so that the \(y\) terms cancel out. Adding the two equations:

   \[
   (5x + y) + (6x - y) = 12 + 10
   \]

   Simplifying:

   \[
   5x + 6x = 22
   \]

   This gives:

   \[
   11x = 22
   \]

2. **Solve for \(x\)**:

   \[
   x = \frac{22}{11} = 2
   \]

3. **Substitute \(x = 2\) into one of the original equations**:
   We'll use the first equation \( 5x + y = 12 \):

   \[
   5(2) + y = 12
   \]

   Simplifying:

   \[
   10 + y = 12
   \]

   Solving for \(y\):

   \[
   y = 12 - 10 = 2
   \]

### Final Solution:

The solution to the system is \( x = 2 \) and \( y = 2 \).

---

Would you like a detailed explanation of any particular step?

Here are 5 related questions:
1. How would the solution change if the system had different coefficients?
2. Can you solve the same system using the substitution method?
3. What happens if both equations have the same slope?
4. Can systems of equations have no solutions? How can we tell?
5. How can we use matrices to solve systems of equations?

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

Solve the system of equations by the addition method: 5x + y = 12, 6x - y = 10.

Learn how to solve the system of linear equations 5x + y = 12 and 6x - y = 10 using the addition method. This step-by-step guide explains key algebraic concepts and provides a clear solution 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