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Learning Goal
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Prove system equivalence
Start lessonBegins with Prove system equivalence · Slides
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
HSA.REI.C.5
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What you'll learn
- 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
Slides
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Prove system equivalence
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