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System of Equations Calculator

Solve systems of 2, 3 or more linear equations (x, y, z …) typed naturally, e.g. 2x + 3y = 13, x − y = −1.

Enter values

Results update as you type.

Result

x

4.6

Solved by Gaussian elimination: x = 4.6, y = -2, z = -1.8.

y
-2
z
-1.8

About the System of Equations Calculator

Solve systems of 2, 3 or more linear equations (x, y, z …) typed naturally, e.g. 2x + 3y = 13, x − y = −1.

Also known as: simultaneous equations, system of linear equations, solve two equations, 3 variable system, linear system solver.

How to use this calculator

  1. Enter equations (one per line).
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

A·x = b ⇒ x = A⁻¹·b (Gaussian elimination)

Worked example

Using the values pre-filled in the calculator above:

  • Equations (one per line): 2x + 3y - z = 5 x - y + 2z = 3 3x + y + z = 10

the calculator returns:

  • x: 4.6
  • y: -2
  • z: -1.8

Frequently asked questions

What if the calculator says the matrix is singular?

The equations are dependent or inconsistent — there is either no solution or infinitely many. Check that each equation adds new information.