Solving Systems of Equations Worksheets

Solving Systems of Equations Worksheet Generator

Choose a topic and options, then print the worksheet. Each worksheet comes with its own answer key.

Special cases
Answer key
Answer key
Enter the same code and options to get the same worksheet again.

Types of systems worksheets you can make:

  • Solving by graphing: students graph two equations on a blank grid and write the solution. The answer key draws both lines and marks where they cross.
  • Reading solutions from graphs: the lines are already drawn, and students read the point where they cross.
  • Solving by substitution: like y = −2x + 2 and 5x + 3y = 5, solution (1, 0)
  • Solving by elimination: from systems where one variable cancels right away, up to multiplying both equations and equations like 7x = 3y + 1
  • Any method (mixed): substitution and elimination problems together
  • No solution and infinitely many solutions: an optional checkbox mixes in these special cases. On graphs they show up as parallel lines or lines that lie on top of each other.
  • Word problems: two numbers pens and notebooks tickets coins fruit prices rectangles gym plans mixtures The answer key can also show what x and y stand for and the system of equations.
  • Three equations with three variables: like x − y + 3z = −13, 2x + 3y − z = −16, −2x − y − 2z = 21, solution (−3, −5, −5)

Make each worksheet your own:

  • four difficulty levels, from whole-number slopes and easy cancelling up to fraction slopes, standard form and larger numbers
  • choose how many problems to include
  • every worksheet comes with an answer key

Solving systems of equations worksheets: a few things to keep in mind and/or remember.

Solving systems of linear equations worksheets

What is solving by the substitution method?

You can solve by substitution when you plug in either the value of x or the value of y into one of the two equations.

Example:

x = y + 1

y + x = 21

Here, you can just replace the value of x or y + 1 in y + x = 21

y + y + 1 = 21

2y + 1 = 21

2y = 20

y = 10 and x  = y + 1 = 10 + 1 = 11 

What is solving by elimination method?

You can solve by elimination when you eliminate either x or y by adding the two equations. We may need to rewrite one or both equations!

Example:

x = y + 1

y + x = 21

Let us rewrite x = y + 1 as x - y = 1 and then add the two equations to eliminate y.

x - y = 1

y + x = 21

Let us add the two equations.

2x - y + y = 1 + 21

2x + 0 = 22

2x = 22

x = 11

Using y + x = 21, y + 11 = 21, so y = 21 - 11 = 10.

Writing equations worksheet