THE NUMBERS, EXPLAINED
How to use this calculator.
Solves two linear equations. Singular systems are reported without a unique numeric solution.
Start with your inputs
Enter x coefficient 1, y coefficient 1, right side 1, x coefficient 2, y coefficient 2, right side 2. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| x coefficient 1 | 1 |
| y coefficient 1 | 1 |
| Right side 1 | 5 |
| x coefficient 2 | 1 |
| y coefficient 2 | -1 |
| Right side 2 | 1 |
A worked example
With the example inputs above, solution is x = 3; y = 2. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Solution | x = 3; y = 2 |
How this is calculated
Solution
solveTwoEquations(a,b,c,d,e,f)
Symbols and units
- a
- x coefficient 1
- b
- y coefficient 1
- c
- Right side 1
- d
- x coefficient 2
- e
- y coefficient 2
- f
- Right side 2
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
For ax + by = c and dx + ey = f, let D = ae − bd. Then x = (ce − bf)/D and y = (af − cd)/D. Reject |D| below 10^−12 rather than presenting a numerically unstable unique solution.
Assumptions and limits
Solves two linear equations. Singular systems are reported without a unique numeric solution.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Solution. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Solves two linear equations. Singular systems are reported without a unique numeric solution.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →