Mississippi Math A-REI.5

MathGrades 9–12Seeing Structure in Expressions

The Standard

Given a system of two equations in two variables, show and explain why the sum of equivalent forms of the equations produces the same solution as the original system.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Solve Systems of Equations

Teacher's field guide

What This Standard Means

What Students Need to Do: Students add two equations and keep one original equation to make a new system. They explain why a solution to either system must also solve the other.
What Mastery Looks Like: Given x+y=7 and x-y=1, a student adds them to get 2x=8 and keeps x-y=1. They find (4,3) and show that subtracting x-y=1 from 2x=8 recovers x+y=7.
Common Misconceptions: Some students keep only the summed equation and lose the second condition. Others add the left sides but forget to add the right sides. Some check their answer in the sum but not in both original equations.
How to Assess It: Exit ticket: For x+y=9 and x-y=3, replace one equation with their sum and solve the new system. Show how to recover the replaced equation.

Lesson moves

Ways to Teach It

Give students cards reading x+y=7 and x-y=1; have them write the sum on a third card and keep one original card.
Ask partners to write how subtracting x-y=1 from 2x=8 recovers x+y=7.
Play 'Same solutions': teams compare 2x=8 alone and 2x=8 with x-y=1 against the original pair.
Use lunch receipts: two sandwiches and a drink cost $13; one sandwich and a drink cost $8; add totals, keep one receipt, and find prices.

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