Simultaneous Equations Calculator
Solve 2, 3 or more linear equations at once, with the elimination steps.
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How to use this calculator
Type each equation on its own line, for example 2x + 3y = 12 and x − y = 1. The solution and the elimination steps appear below.
How it's calculated
The equations are solved by Gauss–Jordan elimination: add or subtract multiples of one equation from another to remove a letter at a time, until each letter is isolated. If the equations contradict each other there is no solution; if they say the same thing there are infinitely many.
Worked example
2x + 3y = 12 and x − y = 1. Multiply the second by 3 to get 3x − 3y = 3. Add it to the first: 5x = 15, so x = 3. Then y = 2. Check: 2(3) + 3(2) = 12 ✓ and 3 − 2 = 1 ✓
Frequently asked questions
What does infinitely many solutions mean?
The equations describe the same line (or plane), so every point on it works. The answer is shown with one letter free.
Can I solve 3 equations with 3 unknowns?
Yes. Put each equation on its own line.
What about equations with x² in them?
Those are not linear. This tool handles straight-line equations only for now.
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Last updated October 2026. Results are for learning and guidance; always check important work. Calculations run in your browser and are not stored.