Problem preview

A-REI.5 Warmup M1-011-A09-V02

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

Show that an original system and transformed system share the same ordered-pair solution

Problem

Solve the original system \(2x~+~y~=~8\) and \(x~+~y~=~5\) and the transformed system \(x~=~3\) and \(x~+~y~=~5\). Give the shared ordered-pair solution and verify it in both systems.

Answer choices

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(3,2); no verification in either system is needed.

(3,1); it satisfies both systems.

(3,2); it satisfies all equations in both systems.

(2,3); it satisfies both systems.

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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: Show that an original system and transformed system share the same ordered-pair solution