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 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.
Ready-made English PDF · fixed settings
Customization below makes a separate PDF.
Fixed English ready-made files. Custom settings below apply only to the configured PDF.
Ready to print
Start with a ready-made worksheet
Graph both equations on the same grid. Identify their intersection, record its coordinates and check the point in both 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
Two lines, one shared solution
Every student task starts with two equations and a blank unit grid from −5 to 5. Draw both lines, identify their intersection and record the ordered pair. The separate key shows the two labeled lines and their shared solution.
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
Interpret the intersection of two lines as the ordered pair that satisfies both equations.
Worked example
Where do y = (1/2)x + 1 and y = −x + 4 meet?
They intersect at (2, 2).
At x = 2, the first equation gives y = 1 + 1 = 2 and the second gives y = −2 + 4 = 2. The same point lies on both lines.
Teaching notes
Make the practice count
- Plot two accurate points for each line.
- Keep the two equations labeled while drawing.
- Read the horizontal coordinate before the vertical coordinate.
- Verify the plotted intersection algebraically if a thick line makes its position unclear.
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 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.
Preview and download