Page 2: Advanced Elimination Examples

This page demonstrates more complex applications of the elimination method, showing how to handle equations with different coefficients and variables.

Vocabulary: LCM (Least Common Multiple) - Used when coefficients need to be matched for elimination

Example: For the system: 2x + 4y = 1 2x - y = 6 Solve by first aligning coefficients of x, then subtracting equations

Highlight: When working with fractions, multiply equations by appropriate factors to create whole numbers before elimination

Page 3: Substitution Method

The substitution method offers an alternative approach to solving systems of equations by expressing one variable in terms of another.

Definition: Substitution involves solving for one variable in terms of another and replacing it in the second equation.

Example: For the system: 2x + 3y = 10 5x - y = 2 Solve by expressing y in terms of x: y = -x + 10

Highlight: The substitution method is particularly useful when:

• One variable has a coefficient of 1
• One equation is already solved for a variable
• Direct elimination would be more complicated

Page 1: System of Equations - Elimination Method

The elimination method follows a structured approach to solving systems of equations by strategically removing variables. This page outlines the fundamental steps and provides practical examples.

Definition: The elimination method involves manipulating two equations to cancel out one variable, allowing you to solve for the remaining variable.

Highlight: The five key steps for elimination method are:

1. Write equations in standard form
2. Choose variable to eliminate
3. Solve for remaining variable
4. Substitute to find second variable
5. Verify solution

Example: Consider the system: 5x + 2y = 1 5x + 3y = 11 By subtracting equations, we eliminate x and solve for y=2