Vocabulary

Variable: A symbol, usually a letter, used to represent a number in mathematical expressions or sentences.

Associative property: The associative property states that you can add or multiply regardless of how the numbers are grouped.

Commutative property: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

Eliminate: To remove or cancel out completely.

Concept

Add two equations vertically without solving for a variable.

Rule

To add equations, use the commutative and associative property to combine like terms.

Example

Choose the correct sum of the given equations.

 3x + 7y = 10
+ x + 7y = 14

Solution

To add equations, you use the commutative and associative property to combine like terms.
(3x + x) + (7y - 7y) = (10 + 14)
4x + 0y = 24
4x = 24

Pre-requisite Skills

Add Linear Expressions (7.5.8)

Properties of Addition (5.3.5)