Georgia 8.FGR.7.4
The Standard
Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.
Georgia's K-12 Mathematics Standards · Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve two equations together using substitution or elimination. They choose an efficient method, show equivalent algebraic steps, and check that the ordered pair satisfies both equations.
What Mastery Looks Like
- Students find an exact ordered-pair solution, including fractional solutions, using clear algebraic steps. They select substitution or elimination efficiently and verify the result in both original equations.
Common Misconceptions
- Students may change only one side of an equation, mishandle negative signs, or distribute incorrectly during substitution. They may stop after finding one variable or fail to check the ordered pair in both equations.
How to Assess It
- Exit ticket: Solve 2x + 3y = 13 and 4x − y = 5 algebraically. Show your steps, name your method, and verify the solution.
Lesson moves
Ways to Teach It
Students model x + y = 5 and x − y = 1 with algebra tiles, then combine the models to eliminate y.
Ask students to compare substitution and elimination for one system, then write which method is more efficient and why.
Run a card sort matching systems, efficient methods, algebraic steps, and exact solutions, with students correcting any unmatched cards.
Students write and solve a system using two school concert ticket purchases to determine the adult and student ticket prices.
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Printable 8.FGR.7.4 Worksheet
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Related Standards
- 8.FGR.7
Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.
- 8.FGR.7.2
Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of...
- 8.FGR.7.3
Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection
- 8.FGR.7.1
Interpret and solve relevant mathematical problems leading to two linear equations in two variables.
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