Back to Prove system equivalence — Problem 3 · 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

In the proof of Direction 1, we let $(x_0, y_0)$ be "any solution" of
the original system.

Why does the proof use "any solution" instead of a specific pair like
$(3, 1)$ ?

Because specific values would make the arithmetic too complicated.

Because the proof must work for every possible solution, and using
"any solution" proves it for all of them at once.

Because the solution $(3, 1)$ does not satisfy the original system.

Because we do not know what the solution is before solving the system.