System of Equations Solver
Type your equations as you would write them — 2x + 3y − z = 5 — and get the solution, or find out if there is no solution or infinitely many.
Result
Enter one equation per line.
How to use this calculator
- Enter one equation per line, using letters for the variables.
- Variables can appear on both sides, such as 2x = y + 1.
Formula
The equations are turned into a coefficient matrix and solved by Gaussian elimination with partial pivoting. A contradiction means no solution; fewer independent equations than unknowns means infinitely many.
Worked example
Three equations
x + y + z = 6, 2y + 5z = −4 and 2x + 5y − z = 27 give x = 5, y = 3, z = −2.
Assumptions and limitations
- Everything runs in your browser; nothing you enter is uploaded or stored.
- Only linear equations are supported (no x², xy or 1/x terms).
Frequently asked questions
What does “infinitely many solutions” mean?
Some equations repeat the same information, so the variables can take many values that all satisfy them.
Can I use variable names other than x, y and z?
Yes — any letters, such as a, b and c.