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Combining Equations in Systems

Jun 19, 2025

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.