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Worksheets›Grade 8›Linear equations & systems›Systems of equations

Systems of Equations Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Grade 8CCSS 8.EE.C.8bAnswer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Both equations solved for y

  1. 1.y = −x + 4y = −2x + 7
  2. 2.y = −2x + 18y = 2x − 14
  3. 3.y = −3x + 22y = 2x − 13
  4. 4.y = −3x + 15y = x − 1
  5. 5.y = −4x + 23y = 4x − 17
  6. 6.y = −3x + 22y = −4x + 29
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

The solution of a system is the point that makes both equations true. Substitute one equation into the other, or add the equations to eliminate a variable.

Easyy = x + 5y = 4x − 1Both equations solved for yMediumx + y = −23x − y = −2Elimination with ±1 coefficientsHard−2x − 6y = −24−3x + 5y = 6General coefficients

How to solve it: a worked example

Solve each system. Write the solution as (x, y).

  1. Starty = 2x − 2y = 3x − 5
  2. Set the right sides equal2x − 2 = 3x − 5
  3. Thenx = 3
  4. Substitute into the first equationy = 2(3) − 2 = 4
  5. Answer(3, 4)

Common mistakes to watch for

  • Solving for x and stopping without finding y.
  • Adding the equations without first lining up like terms.
  • Multiplying only one side of an equation when scaling it for elimination.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Multi-step equationsEquations with variables on both sidesLaws of exponentsScientific notationSquare roots & cube roots

FAQ

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix systems of equations with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.