System of equations solver
Two or three equations, solved the way you learn it.
Output
Paste or type above to see the result here.
Your files stay on your device
This tool runs entirely in your browser. What you paste is processed on your device and is never sent to a server, so it is safe to use with tokens, keys and unpublished text.
How it works
- Type each equation on its own line: two with x and y, or three with x, y and z. Fractions, decimals and brackets are fine.
- Choose the method for two equations, or leave it on automatic; three equations are solved by Gaussian elimination.
- The solution comes first, then every step with the equations numbered, and a check in each equation.
Frequently asked questions
- Which method is best?
- Substitution is quickest when an unknown already stands alone or has 1 in front of it; elimination when the numbers line up; Cramer’s rule gives the answer by determinants in one go. All give the same solution.
- What if the system has no solution?
- Then the two lines are parallel — same slope, different intercept — and never meet. If the equations describe the same line, every point on it is a solution; the solver shows which case it is.
- How are three equations solved?
- By Gaussian elimination: x is removed from the second and third equations, then y from the third, and z, y and x are found from the bottom up.
- Can I write the equations in any form?
- Yes: y = 2x + 1, 3x + 2y − 7 = 0 or x/2 + y = 3 are rearranged first, and the rearranged forms are shown.
- Is anything uploaded?
- No. It is worked out in your browser, and nothing you type leaves your computer.
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