**Adding Expressions by Horizon Method**

Horizon method is a method used to add or subtract algebraic expressions that have the same variable and degree. The method involves aligning the coefficients of the like terms in a column and then adding or subtracting them to arrive at the final answer. In this article, we will discuss how to add expressions using the horizon method.

**Steps to Add Expressions using Horizon Method**

The following are the steps to follow when adding expressions using the horizon method:

Step 1: Write the expressions in a column such that the like terms are aligned.

Step 2: Add the coefficients of the like terms vertically.

Step 3: Write the sum of the coefficients with the variable.

Step 4: Simplify the expression if possible.

**Example 1**

Add 3x + 5y and 2x - 7y

Step 1: Write the expressions in a column such that the like terms are aligned.

3x + 5y

2x - 7y

Step 2: Add the coefficients of the like terms vertically.

3x + 5y

+ 2x - 7y

--------

5x - 2y

Step 3: Write the sum of the coefficients with the variable.

5x - 2y

Step 4: Simplify the expression if possible.

The expression 5x - 2y is in its simplest form and cannot be further simplified.

**Example 2**

Add 4x^2 - 3x + 2 and 2x^2 + 5x - 1

Step 1: Write the expressions in a column such that the like terms are aligned.

4x^2 - 3x + 2

2x^2 + 5x - 1

Step 2: Add the coefficients of the like terms vertically.

4x^2 - 3x + 2

+ 2x^2 + 5x - 1

-----------------

6x^2 + 2x + 1

Step 3: Write the sum of the coefficients with the variable.

6x^2 + 2x + 1

Step 4: Simplify the expression if possible.

The expression 6x^2 + 2x + 1 is in its simplest form and cannot be further simplified.

**Conclusion**

Adding expressions using the horizon method is a simple process that involves aligning the like terms and adding the coefficients vertically. The method is useful in simplifying algebraic expressions and solving equations.