System of linear equations solver
Type one equation per line, such as 2x + 3y = 7 and x − y = 1, and get the solution. The calculation uses exact fractions, so 1/3 stays 1/3 instead of 0.333….
One equation or a system, with unknowns such as x, y and z. Fractions such as 1/2 are allowed.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
How to enter equations
- One equation per line, each with exactly one
=. - Use any letters as unknowns: x, y, z, or a, b, c.
- Multiplication signs are optional:
3xis 3 × x. Terms may be on both sides, such as2x + 1 = y − 3.
Three possible outcomes
- One solution: for 2x + 3y = 7 and x − y = 1 you get x = 2 and y = 1.
- No solution: the equations contradict each other, like x + y = 1 and x + y = 5.
- Infinitely many solutions: an equation is a combination of the others; you see which unknowns you can choose freely.
The method is Gauss-Jordan elimination, the same row reduction you would do on paper. Equations with x² or sin(x) are not linear; for one quadratic equation, use the quadratic equation solver.
Frequently asked questions
Is the system of equations solver free?
Yes. The system of equations solver is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.