What is the Simultaneous Equations Solver?
Solve two linear equations in two unknowns: a₁x + b₁y = c₁ and a₂x + b₂y = c₂.
Enter a₁, b₁, c₁, a₂, b₂ and c₂ and the Simultaneous Equations Solver returns solution and determinant. Results update as you type, and nothing you enter leaves your device.
How it is calculated
Cramer's rule: x = (c₁b₂ − c₂b₁) ÷ D and y = (a₁c₂ − a₂c₁) ÷ D, where D = a₁b₂ − a₂b₁
How to use it
- Enter a₁.
- Enter b₁.
- Enter c₁.
- Enter a₂.
- Enter b₂.
- Enter c₂.
- Read solution in the results panel. It updates as you type.
- Change any value to compare scenarios, or use Share to send the result as a link.
Worked example
Common questions
What formula does the Simultaneous Equations Solver use?
It uses: Cramer's rule: x = (c₁b₂ − c₂b₁) ÷ D and y = (a₁c₂ − a₂c₁) ÷ D, where D = a₁b₂ − a₂b₁.
What do I need to use the Simultaneous Equations Solver?
You need a₁, b₁, c₁, a₂, b₂ and c₂. Sensible starting values are filled in so you can see how it works straight away.
Is the Simultaneous Equations Solver free, and is my data stored?
It is free with no sign-up. The calculation runs in your browser, so the values you enter are not sent to or stored on our server.