Two Linear Equations Calculator
Two Linear Equations: calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system.
Example Calculation
- a₁ in a₁x+b₁y=c₁: 1
- b₁: 1
- c₁: 5
- a₂: 1
- b₂: -1
- c₂: 1
x + y = 5 and x − y = 1 have solution x = 3, y = 2.
Frequently asked questions
How do I use this calculator?
Enter a₁ in a₁x+b₁y=c₁, b₁, c₁, a₂, b₂, c₂. The result updates automatically. Use Reset to restore the example values.
What method does it use?
D = a₁b₂−a₂b₁; x = (c₁b₂−c₂b₁)/D; y = (a₁c₂−a₂c₁)/D. Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.