Simultaneous Equations Calculator
Solve two linear equations in x and y. See determinants, substitution checks and the two lines, including parallel or coincident cases.
YOUR CALCULATION
Result
β
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the determinant Ξ = ae β bd. When it is nonzero, x = (ce β bf)/Ξ and y = (af β cd)/Ξ. Substitute both results into the original equations to check them. A zero determinant needs a consistency check rather than division by zero.
Ξ = ae β bd; x = (ce β bf)/Ξ; y = (af β cd)/Ξ
Worked example
x + y = 5 and x β y = 1 have Ξ = β2, x = 3 and y = 2. Their lines intersect at (3, 2).
Assumptions and input details
Identical equations have infinitely many common solutions. Inconsistent parallel equations have none. A row such as 0x + 0y = 1 is inconsistent even if the other row contains no variables.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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