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A-REI.5 Warmup M1-011-A01-V04

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

Verify that replacing an equation in a system preserves a solution

Problem

The original system is \(x+2y=8\) and \(x-y=2\). Subtracting the second equation from the first and retaining \(x-y=2\) gives the transformed system \(x-y=2\) and \(3y=6\). Given that \((4,2)\) solves the original system, test it in both transformed equations: identify each left/right value and still-a-solution yes/no.

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Four variants of this problem type
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
Verify that replacing an equation in a system preserves a solution