How it works
Enter the coefficients and right-hand constants in the stated equation order. The system 2x + y = 5 and x − y = 1 has x = 2 and y = 1. A zero determinant means there is no unique solution. Systems with a determinant tiny relative to its forming products are also rejected to avoid unstable division.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| a in ax + by = c | 2 | Enter a numeric value. |
| b in ax + by = c | 1 | Enter a numeric value. |
| c in ax + by = c | 5 | Enter a numeric value. |
| d in dx + ey = f | 1 | Enter a numeric value. |
| e in dx + ey = f | -1 | Enter a numeric value. |
| f in dx + ey = f | 1 | Enter a numeric value. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- a in ax + by = c
- 2
- b in ax + by = c
- 1
- c in ax + by = c
- 5
- d in dx + ey = f
- 1
- e in dx + ey = f
- -1
- f in dx + ey = f
- 1
Complete example results
- Solution x
- 2
- Solution y
- 1
- Determinant
- -3
Reading the result
Use quantities on the same basis. The starting value in percentage change, the denominator in a ratio and the length unit in geometry determine the meaning of the answer. Check the formula conditions alongside the example.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
How can I check the returned solution?
Substitute x and y into both original equations. Both left sides should match their respective constants, allowing for displayed rounding.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.