Back to Prove system equivalence — Problem 1 · Task Set 39

HSA.REI.C.5 Tutor Intake — Proving System Equivalence

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Grade 9·7 problems·~11 min·Common Core Math - HS Algebra·standard·hsa-rei-c-5

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Concepts

The system-equivalence theorem (REI.C.5) says: replacing one equation $E_1$
in a system with $E_1 + k \cdot E_2$ produces an equivalent system.

What does "equivalent system" mean?

The equations in the new system look the same as the original equations.

The new system has the same solution set as the original system.

The new system has the same number of equations.

The new equation $E_1 + k \cdot E_2$ is a true statement.