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Two simultaneous linear equations Calculator
Solve two linear equations in x and y, with controlled errors for singular or ill-conditioned systems. This free two simultaneous linear equations calculator shows the calculation and its assumptions so you can compare your own figures.
Your results
Solve two linear equations in x and y, with controlled errors for singular or ill-conditioned systems.
Calculated outcomes
- Determinant
- -3
Assumptions and estimates
- Solves ax + by = c and dx + ey = f. Singular or numerically ill-conditioned systems return a controlled error instead of an unreliable answer.
- Method: For ax + by = c and dx + ey = f, determinant = ae − bd; x = (ce − bf)/determinant; y = (af − cd)/determinant.
- Singular/inconsistent or numerically ill-conditioned systems cannot produce a reliable unique answer and return a controlled error. Signed coefficients are supported.
Useful next steps
- Use Compare options to test an alternative side by side.
- Copy, print or download a record of this calculation when you need one.
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How the two simultaneous linear equations calculation works
For ax + by = c and dx + ey = f, determinant = ae − bd; x = (ce − bf)/determinant; y = (af − cd)/determinant.
Singular/inconsistent or numerically ill-conditioned systems cannot produce a reliable unique answer and return a controlled error. Signed coefficients are supported.
Using this calculator
- Enter your own figures in the labelled inputs. Keep the currencies, units and time periods consistent.
- Choose any applicable rate profile, pattern or assumption shown for this tool. Open additional inputs when relevant.
- Review x and y, then read the stated assumptions and eligibility conditions before using the result.
Worked example
This is a static example using illustrative inputs, not facts about you or today’s date. The displayed eligibility selections and assumptions apply only to this example.
See example inputs
- Equation 1: x coefficient a
- 2
- Equation 1: y coefficient b
- 1
- Equation 1: right side c
- 5
- Equation 2: x coefficient d
- 1
- Equation 2: y coefficient e
- -1
- Equation 2: right side f
- 1
- X
- 2
- Y
- 1