Overview
This lesson covers the technique of combining equations in systems of equations, specifically adding two equations together to simplify or solve the system.
Combining Equations in Systems
- When solving a system, you can add two equations together to combine like terms and eliminate variables.
- Example equations: 5xy = 6 and 2x + y = 8.
- Adding equations helps in using the elimination method, especially when coefficients align to cancel out variables.
- The goal is to reduce the system to a single equation in one variable.
Elimination Method Strategy
- The elimination method involves combining equations to eliminate one variable.
- Adjust equations, if necessary, by multiplying to align coefficients before adding or subtracting.
- Once a variable is eliminated, solve the remaining equation for the other variable.
- Substitute back to find the value of the eliminated variable.
Key Terms & Definitions
- System of Equations — a set of two or more equations with the same variables.
- Elimination Method — a technique to solve systems by adding or subtracting equations to remove a variable.
- Variable — a symbol (usually x or y) that represents an unknown number.
Action Items / Next Steps
- Practice combining equations using the elimination method with at least four problems.
- Review related videos on elimination strategies for a deeper understanding.