Prove system equivalence

What you'll learn

1. State the system-equivalence theorem: replacing one equation in a system by the sum of that equation and a multiple of another produces an equivalent system
2. Prove the theorem in both directions: any solution of the original system satisfies the new equation, and any solution of the new system satisfies the original equations
3. Explain why the elimination method for solving systems of linear equations is justified by this theorem
4. Use the theorem to perform legal elimination steps and identify which operations preserve system equivalence
5. Connect the proof technique to the properties of equality used in single-equation solving

Prerequisites

• Explain equation solving steps