Worksheets · Algebra 1

Solving systems by graphing worksheet

Draw both lines on the grid; the solution is the point they share. Every crossing here is at whole-number coordinates, so once the lines are drawn it can be read straight off the grid. Easy gives two whole slopes, medium makes one a fraction, and hard prints one line in standard form to be rearranged first.

Select your difficulty

Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems by Graphing

Date Period

Graph both lines and find where they cross.

  1. Graph both lines and find where they cross: y=3x+18 and y=−43x−8-10-10-5-55510100
  2. Graph both lines and find where they cross: y=−x+6 and y=−13x+6-10-10-5-55510100
  3. Graph both lines and find where they cross: y=−x+1 and y=−32x+3-10-10-5-55510100
  4. Graph both lines and find where they cross: y=2x+2 and y=13x−3-10-10-5-55510100
  5. Graph both lines and find where they cross: y=x+4 and y=13x+4-10-10-5-55510100
  6. Graph both lines and find where they cross: y=−3x−9 and y=12x−2-10-10-5-55510100
  7. Graph both lines and find where they cross: y=−x−4 and y=52x+17-10-10-5-55510100
  8. Graph both lines and find where they cross: y=3x−4 and y=−13x+6-10-10-5-55510100
  9. Graph both lines and find where they cross: y=3x+14 and y=13x+6-10-10-5-55510100
  10. Graph both lines and find where they cross: y=x−11 and y=−13x−3-10-10-5-55510100
  11. Graph both lines and find where they cross: y=2x+6 and y=−52x−3-10-10-5-55510100
  12. Graph both lines and find where they cross: y=−3x−13 and y=−13x−5-10-10-5-55510100
  13. Graph both lines and find where they cross: y=−x−2 and y=−23x−2-10-10-5-55510100
  14. Graph both lines and find where they cross: y=2x−11 and y=−43x−1-10-10-5-55510100
  15. Graph both lines and find where they cross: y=x and y=−12x+9-10-10-5-55510100
  16. Graph both lines and find where they cross: y=x+6 and y=−53x−2-10-10-5-55510100
  17. Graph both lines and find where they cross: y=−3x+5 and y=−53x+1-10-10-5-55510100
  18. Graph both lines and find where they cross: y=−2x+8 and y=−23x+4-10-10-5-55510100
  19. Graph both lines and find where they cross: y=−x+12 and y=−12x+9-10-10-5-55510100
  20. Graph both lines and find where they cross: y=−3x−12 and y=−53x−8-10-10-5-55510100

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Systems by GraphingAnswer keyVersion 1

Date Period

Graph both lines and find where they cross.

  1. Graph both lines and find where they cross: y=3x+18 and y=−43x−8-10-10-5-55510100(−6,0)
  2. Graph both lines and find where they cross: y=−x+6 and y=−13x+6-10-10-5-55510100(0,6)
  3. Graph both lines and find where they cross: y=−x+1 and y=−32x+3-10-10-5-55510100(4,−3)
  4. Graph both lines and find where they cross: y=2x+2 and y=13x−3-10-10-5-55510100(−3,−4)
  5. Graph both lines and find where they cross: y=x+4 and y=13x+4-10-10-5-55510100(0,4)
  6. Graph both lines and find where they cross: y=−3x−9 and y=12x−2-10-10-5-55510100(−2,−3)
  7. Graph both lines and find where they cross: y=−x−4 and y=52x+17-10-10-5-55510100(−6,2)
  8. Graph both lines and find where they cross: y=3x−4 and y=−13x+6-10-10-5-55510100(3,5)
  9. Graph both lines and find where they cross: y=3x+14 and y=13x+6-10-10-5-55510100(−3,5)
  10. Graph both lines and find where they cross: y=x−11 and y=−13x−3-10-10-5-55510100(6,−5)
  11. Graph both lines and find where they cross: y=2x+6 and y=−52x−3-10-10-5-55510100(−2,2)
  12. Graph both lines and find where they cross: y=−3x−13 and y=−13x−5-10-10-5-55510100(−3,−4)
  13. Graph both lines and find where they cross: y=−x−2 and y=−23x−2-10-10-5-55510100(0,−2)
  14. Graph both lines and find where they cross: y=2x−11 and y=−43x−1-10-10-5-55510100(3,−5)
  15. Graph both lines and find where they cross: y=x and y=−12x+9-10-10-5-55510100(6,6)
  16. Graph both lines and find where they cross: y=x+6 and y=−53x−2-10-10-5-55510100(−3,3)
  17. Graph both lines and find where they cross: y=−3x+5 and y=−53x+1-10-10-5-55510100(3,−4)
  18. Graph both lines and find where they cross: y=−2x+8 and y=−23x+4-10-10-5-55510100(3,2)
  19. Graph both lines and find where they cross: y=−x+12 and y=−12x+9-10-10-5-55510100(6,6)
  20. Graph both lines and find where they cross: y=−3x−12 and y=−53x−8-10-10-5-55510100(−3,−3)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Graph both lines and find where they cross: y=2x−1 and y=−x+5

  1. Draw y = 2x - 1: start at -1, up 2 across 1.
  2. Draw y = -x + 5: start at 5, down 1 across 1.
  3. They share (2, 3). Check it in both.

The answer is (2,3).

Where students go wrong

Reading the coordinates the wrong way round, or giving only one number. The answer is a point, so it needs both, and across comes before up.

Also called graphing method, intersection of two lines or systems of equations.

Questions about these worksheets

Yes. Every solving systems by graphing sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the solving systems by graphing questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Reading the coordinates the wrong way round, or giving only one number. The answer is a point, so it needs both, and across comes before up.