Solve two equations with two unknowns

Students and technicians use it to solve two equations with two unknowns when checking an exercise or a simple model.

Solve two equations with two unknowns. Everything runs in your browser, so the values you enter are never uploaded, shared, or stored.

How to use

Identify the coefficients of your two equations in the form ax + by = c and dx + ey = f.
Enter the six values in the expected order, keeping positive and negative signs correct.
Run the solver to obtain the values of the two unknowns.
Check that the proposed pair satisfies both original equations.
If there is no unique solution, read the displayed message before drawing a conclusion.

Example

The sample describes the system x + y = 3 and x - y = 1. After solving, substitute the proposed values into both equations to confirm that the result is consistent.

Input

Output

Determinant: -2
x: 2
y: 1

Limits and formats

The tool handles only two equations with two unknowns, not larger systems.
It may show the solution or an error message rather than every intermediate calculation step.
Incorrect coefficients or a reversed order will distort the answer; review all six values before submitting.
A system can have no solution or infinitely many solutions, so interpret the output in that light.
Imported files must contain usable numbers, even if several text extensions are accepted.

Where processing happens

The solving process takes place in your browser. The coefficients you type or import stay on your device and are not sent anywhere else. That lets you test a homework exercise or check a simple model without creating an account or storing the values.

Frequently asked questions

What do a, b, c, d, e, and f mean?

They are the coefficients of two equations written as ax + by = c and dx + ey = f. Enter the six numbers in that order so the solver can interpret the system correctly.

Why is there no unique solution?

The two lines may be parallel and never meet, or they may coincide and share infinitely many points. In those situations, there is not one single pair of values for the unknowns.

Can I enter fractions or decimals?

You can try decimal numbers if the field accepts them. For schoolwork, it is often easier to enter a decimal approximation and then verify the result with exact fraction arithmetic.