System of 2 linear equations solver
Write each equation as ax + by = c and enter its coefficients. You get x and y along with the determinant.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter a1 (x in equation 1), b1 (y in equation 1), c1 (constant 1), a2 (x in equation 2), b2 (y in equation 2) and c2 (constant 2).
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Determinant D = a1·b2 - a2·b1, then x = (c1·b2 - c2·b1) / D and y = (a1·c2 - a2·c1) / D. If D = 0 the lines are parallel (no solution) or identical (infinitely many).
Example
Inputs: a1 (x in equation 1) = 2, b1 (y in equation 1) = 3, c1 (constant 1) = 13, a2 (x in equation 2) = 1, b2 (y in equation 2) = -1. Result: Solution: x = 2, y = 3; x: 2; y: 3.
Limits and caveats
- Linear equations only; terms like x² or xy are not supported.
- Long decimals are rounded for display.
Questions about this tool
How do I enter y = 2x + 1?
Rearrange it to ax + by = c: -2x + y = 1, so a = -2, b = 1, c = 1.
What does a zero determinant mean?
Both lines have the same slope, so they are either parallel and never meet, or they are the same line.
Is the answer the intersection point?
Yes. The solution (x, y) is the point where the two lines cross.