System of Equations Solver
Solve 2×2 and 3×3 simultaneous linear systems.
Solution
x = 2, y = 3
Determinant
-14
Check eq. 1
13
Check eq. 2
5
ShowHide the working
- 1Determinant = 2×-1 − 4×3 = -14
- 2x = (c₁b₂ − c₂b₁) ÷ det = 2
- 3y = (a₁c₂ − a₂c₁) ÷ det = 3
Formula
Cramer's rule for a 2×2 systemHow it works
Solves two simultaneous linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ using Cramer's rule.
Example
2x + 3y = 13 and 4x − y = 5 give x = 2, y = 3.
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About the System of Equations Solver
Solve 2×2 and 3×3 simultaneous linear systems. It sits in the Math & Algebra section of NWS Calc, a free collection of calculators that run entirely in your browser. There is no signup, no paywall and no tracking — open the page, enter your numbers, get an answer.
Frequently asked questions
- Is the System of Equations Solver free to use?
- Yes. Every calculator on NWS Calc is completely free, with no signup, no usage limits and no ads.
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- No. The System of Equations Solver runs entirely in your browser using JavaScript. Nothing you type is uploaded, logged or stored on a server.
- Can I use the System of Equations Solver on my phone?
- Yes. The page is fully responsive and works in any modern mobile or desktop browser — there is nothing to install.
- What else is in Math & Algebra?
- Equations, fractions, primes, roots, sequences and number theory. You can browse the full Math & Algebra category for related calculators.