Common Core Math - HS Algebra
Lesson Plan
Prove system equivalence
Goals / Objectives
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
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
Explain why the elimination method for solving systems of linear equations is justified by this theorem
Use the theorem to perform legal elimination steps and identify which operations preserve system equivalence
Connect the proof technique to the properties of equality used in single-equation solving
Standards
HSA.REI.C.5
Academic Vocabulary
Not in our source material
Enrichment
Accommodations
Not in our source material