Problem preview

A-REI.5 Warmup M1-011-A09-V04

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 \(2x~+~y~=~9\) and \(x~-~y~=~3\) and the transformed system \(3x~=~12\) and \(x~-~y~=~3\). Give the shared ordered-pair solution and verify it in both systems.

Answer choices

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(4,1); it satisfies both systems.

(4,1); no verification in either system is needed.

(4,-1); it satisfies both systems.

(3,4); 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