Problem preview

A-REI.5 Core M1-011-R03-V02

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

Form and verify an elimination row combination

Problem

\(E_{1}\): \(x+2y=8\); \(E_{2}\): \(3x-y=3\). Use \(E_{2}-3E_{1}\).

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combination=3E2-E1; result=8x-5y=1; isolated=y=3; solution=(2,3)

combination=E2-3E1; result=2x-7y=-21; isolated=y=3; solution=(2,3)

combination=E2-3E1; result=-7y=21; isolated=y=-3; solution=(14,-3); checks=pass

combination=E2-3E1; result=-7y=-21; isolated=y=3; solution=(2,3); checks=2+2(3)=8 and 3(2)-3=3

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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: Form and verify an elimination row combination