Problem preview

A-REI.5 Warmup M1-011-A12-V03

Justify elimination: replacing one equation in a two-variable system with a linear combination preserves solutions.

Decide whether an elimination action loses system information

Problem

A transformation replaces both equations of a system with the same sum equation. Classify whether the transformation preserves or loses information, and explain why.

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classification = preserves information; reason = reversible using an unchanged equation

classification = preserves information; reason = two independent sums remain

classification = loses information; reason = nonzero scaling changes solutions

classification = loses information; reason = duplicate sum leaves only one distinct constraint

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Curriculum context

Course: Math I
Standard: A-REI.5
Category: Algebra
Domain: Reasoning with Equations and Inequalities
Objective: Justify elimination: replacing one equation in a two-variable system with a linear combination preserves solutions.
Problem type: Decide whether an elimination action loses system information