Solving Systems of Equations Using Elimination and Substitution Methods

This comprehensive page demonstrates various approaches to solving systems of linear equations through both elimination and substitution methods. The content presents multiple worked examples showing different scenarios and solution strategies.

Definition: The elimination method involves manipulating equations to cancel out one variable, while substitution involves expressing one variable in terms of another.

Example: In the first problem (2x + 3y = 7 and 5x + 4y = 14), the elimination method is demonstrated by multiplying equations by appropriate factors to eliminate variables.

Highlight: When using elimination, equations with same signs should be subtracted, while different signs should be added to cancel out variables.

Vocabulary:

• Elimination Method: A technique where equations are manipulated to cancel out one variable
• Substitution Method: A process where one variable is expressed in terms of another and then substituted
• System of Linear Equations: A set of two or more equations that must be solved simultaneously

Example: Another problem (3x + y = -10 and x + 2y = 6) shows how to use substitution by expressing one variable in terms of another and solving step by step.

The page includes detailed solutions showing intermediate steps, making it easier for students to follow the problem-solving process. Multiple examples demonstrate different scenarios where these methods can be applied effectively.