Printable pre-algebra, algebra and geometry worksheets

Graphing Systems of Equations Worksheet Generator

Print systems of linear equations to solve by graphing, substitution or elimination – the answer key draws both lines and marks the solution.

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The Systems of Equations Worksheet Generator makes printable practice sheets for solving two linear equations at the same time, by graphing, substitution, elimination, or a mix of methods. It is free, needs no sign-up, and runs in your web browser, so the problems are made on your own device and nothing is uploaded. Choose the problem types, difficulty, and number of problems, then print the sheet or save it as a PDF with an answer key. The graphing problems come with a blank coordinate grid under each system, and the same tool covers simultaneous equations in the British sense. Every system it makes has exactly one solution, so each answer can be checked. Everything you make here is free to use in class or in products you sell, such as Teachers Pay Teachers resources, Etsy printables or KDP workbooks.
Graphing systems of equations worksheet example

How to use the Systems of Equations Worksheet Generator

  1. Tick one or more Problem types on the left: Substitution, Elimination, Graphing, or Any method. Graphing is ticked when the page opens.
  2. Choose a Difficulty: Easy, Medium, or Hard.
  3. Choose the Number of problems, from 6 to 30.
  4. Open More options to set the Columns (Automatic, 1, 2, or 3), the Paper size (Letter 8.5 × 11 in or A4 210 × 297 mm), a Worksheet title, and the Name and date line checkbox.
  5. Keep Answer key on a separate page ticked if you want a key. It is on by default.
  6. Check the preview on the right. It shows the sheet as it will print.
  7. Press Show answers to see each answer under its problem in the preview. Press it again to hide them.
  8. Press Print / Save as PDF. In the print dialog, choose Save as PDF if you want a PDF file.

Press New worksheet to get a fresh random set with the same settings. A teacher can print several versions this way. Copy link saves a link that opens exactly the same worksheet again. Your settings are remembered in this browser for your next visit, unless you open a shared link. The tool also works on phones and tablets, but printing needs a printer or the Save as PDF option.

How do you solve a system of equations by graphing

To solve a system by graphing, draw both lines and find where they cross. The crossing point (x, y) is the only pair of values that makes both equations true.

To graph a line, write it as y = mx + b. Start at b on the y-axis, use the slope m (rise over run) to find a second point, and draw the line through both points. Then read the intersection and check it in both equations.

For example, take y = -3x + 6 and y = -x + 4. The lines cross at (1, 3). Check: -3(1) + 6 = 3, and -(1) + 4 = 3. Both are true, so (1, 3) is the solution.

Graphing problems on this page print an empty grid from -8 to 8 under each system, and every intersection is a whole-number point. Hard problems can use fractional slopes such as y = (1/2)x + 4, so plan your steps carefully. A drawn intersection can be hard to read exactly, so always check the point in both equations.

Substitution vs elimination: which to use

Use substitution when one equation is already solved for y or x, or nearly is. Use elimination when the two equations line up well, so that adding or subtracting them removes one variable. Both methods give the same answer.

With substitution, replace the expression in the second equation. For y = x - 4 and x + y = 8, you get x + (x - 4) = 8, so 2x = 12, x = 6, and y = 2. The solution is (6, 2).

With elimination, add or subtract the equations to cancel a variable. For x + y = 5 and 5x - y = 19, add them to get 6x = 24, so x = 4. Then y = 1, and the solution is (4, 1). If no variable cancels, multiply one equation by a number first.

The Any method type prints systems in standard form, so you can choose substitution or elimination for each one.

Sample problems from this generator

  1. y = 4x
    y = −3x − 7    −8−6−4−22468−8−6−4−22468 Answer: (−1, −4)
  2. y = −3x − 2
    y = −x + 2    −8−6−4−22468−8−6−4−22468 Answer: (−2, 4)
  3. y = 3x + 8
    y = −x    −8−6−4−22468−8−6−4−22468 Answer: (−2, 2)
  4. y = −2x − 4
    y = 4x − 4    −8−6−4−22468−8−6−4−22468 Answer: (0, −4)

Frequently asked questions

What does it mean if the lines are parallel?

Parallel lines have the same slope and different y-intercepts, so they never cross. The system has no solution. If both equations describe the same line, there are infinitely many solutions. Every system on this worksheet has exactly one solution, so you will not see either case here.

Are answers included?

Yes. The answer key is on by default under More options. When you print, it starts on a new page after the worksheet and lists every problem number with its answer. Graphing answers are drawn as lines with the intersection marked. Press Show answers to see them in the preview first.

Is a simultaneous equation worksheet the same as a systems of equations worksheet?

Yes. Simultaneous equations is the British name for systems of equations. Both mean two equations with two unknowns that are solved together. The same generator makes both.

Can I save a graphing systems of equations worksheet as a PDF?

Yes. Tick Graphing, press Print / Save as PDF, and choose Save as PDF in the browser’s print dialog. You can also change the paper size to Letter or A4 first.

Can I make new problems without changing the settings?

Yes. Press New worksheet to get a fresh random set with the same settings. No problem repeats on a single sheet.

Does it work on a phone?

Yes, it works on phones and tablets. You can still choose problem types, preview the sheet, and copy a link. Printing needs a printer, or you can use Save as PDF.

Can I use the systems of equations worksheets I make in my tutoring business or my TpT store?

Yes. The worksheets and answer keys you generate are free for personal, classroom and commercial use, such as Teachers Pay Teachers products, Etsy listings or a printed workbook. You do not need to credit this site. You may not copy the generator itself and offer it as your own tool.