Florida B.E.S.T. MA.912.AR.9.9
The Standard
Given a mathematical or real-world context, solve a system of three-variable linear equations algebraically.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students combine equations using elimination or substitution until they can find all three unknown values. They interpret the ordered triple in context and check it in every original equation.
What Mastery Looks Like
- A student can choose useful equation pairs and eliminate the same variable twice. They solve the resulting two-variable system, substitute back, and label the ordered triple correctly. They verify the result in all three original equations.
Common Misconceptions
- Students often lose negative signs when multiplying or subtracting equations. They may eliminate different variables from each pair, leaving an unusable system. Some stop after finding two variables or do not check the ordered triple in every equation.
How to Assess It
- Exit ticket: Solve x + y + z = 6, x - y + z = 2, and x + y - z = 4. Show each elimination step and verify your ordered triple.
Lesson moves
Ways to Teach It
Give groups three colored equation strips; students scale and combine pairs to eliminate the same variable, then solve the resulting system.
Ask students to explain why two elimination steps must remove the same variable, then compare two valid solution paths.
Run an elimination relay where teams complete one step per turn and score only when signs and arithmetic are correct.
Students solve a school play problem using adult, student, and child tickets, total attendance, total revenue, and one category relationship.
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Related Standards
- MA.912.AR.9.1
Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.
- MA.912.AR.9.2
Given a mathematical or real-world context, solve a system consisting of a two-variable linear equation and a non-linear equation algebraically or graphically.
- MA.912.NSO.4.2
Given a mathematical or real-world context, represent and solve a system of two- or three-variable linear equations using matrices.
- MA.912.AR.9.3
Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically.
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