Systems of equations
Systems of equations methods handout
Compare substitution, elimination and graphing in an original printable guide. Choose the methods to include and follow worked examples that check both equations.
Preview and downloadSystems of equations practice
Solving systems of equations worksheets
Solve ten two-variable systems using substitution, elimination or any method. Choose four equation-pair structures and download exact, step-by-step answer keys.
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Start with a ready-made worksheet
Use the requested method to find x and y. Write the answer as an ordered pair and substitute it into both original equations.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetPaper sizes and printing help · More systems of equations activities
Open a focused studio preset
These links set the editable studio below. Download there for the selected settings; ready-made files above keep their default edition.
Follow the transformations, then check
Choose substitution, elimination or any method. The worked key shows the algebra used for each question, retains exact fractions and checks the resulting coordinates in both original equations.
Choose one equation-pair structure when introducing a method. Mix the structures once the learner can select a useful first step and explain why it is valid.
Learning objective
What this activity builds
Solve two linear equations together with equivalent transformations and verify the resulting ordered pair.
Worked example
Solve 3x + 2y = 16 and 2x − 3y = 2 by elimination.
The solution is (4, 2).
Multiply the first equation by 3 and the second by 2. Adding 9x + 6y = 48 and 4x − 6y = 4 gives 13x = 52. Then x = 4, and substitution gives y = 2. Both original equations are true.
Teaching notes
Make the practice count
- Choose a variable to isolate or eliminate before calculating.
- Scale every term and the constant on both sides.
- Keep fractions exact instead of rounding an intermediate result.
- Check the solution in both original equations, not only in a transformed equation.
Choose a systems of equations worksheet by method
Start substitution with the general-and-simple equation preset when learners can isolate a variable and substitute an entire expression. For x + y = 9 and y = 2x, substitute the whole expression 2x for y. Then x + 2x = 9 gives x = 3 and y = 6. The point (3, 6) satisfies both original equations.
Use the two-standard-form equation preset to practice elimination and scaling complete equations. The worked example above requires scaling both equations before cancellation. Once each method is understood, choose any method and ask learners to justify which first step is more efficient.
Do these algebra worksheets include no-solution or infinitely-many-solution systems?
This activity generates systems with one unique solution. The ten-question worked key preserves exact fractional coordinates when they occur and checks both original equations. It is not a classification worksheet for parallel or coincident lines.
How do I print a substitution-only or elimination-only sheet?
Open a method preset on this page and use the editable studio to preview and download it. The ready-made files above use substitution with all four equation-pair structures selected; preset links do not replace those files.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose equation structures and a solving method. Graphing worksheets keep every student coordinate plane blank; answer editions show both numbered lines and their exact intersection.
Enlarged pages scroll. PDF size stays the same.
A useful next step
Related activities
Systems of equations
Solving systems by graphing worksheets
Graph eight pairs of linear equations on blank coordinate grids. Choose equation forms, locate each intersection and check a separate key with both lines and the exact solution.
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