System of Equations Calculator
Last updated: October 15, 2026
Solve two linear equations with two unknowns using the determinant method.
Solution
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- x value: —
- y value: —
- Determinant: —
- Classification: —
On this page
Quick summary: Solve two linear equations with two unknowns using the determinant method.
Read the method, example and limitations
Updated reference sections in this guide are in English.
Guide language: English. Updated October 15, 2026.
What this calculator estimates
Solve two linear equations with two unknowns using the determinant method.
Inputs and units
Enter Equation 1: x coefficient, Equation 1: y coefficient, Equation 1: result, Equation 2: x coefficient, Equation 2: y coefficient, Equation 2: result. Use the units shown. Required fields cannot be blank. Use zero only where that field and the model allow it. Select Calculate after changing the values.
Method and assumptions
For a1 x + b1 y = c1 and a2 x + b2 y = c2, determinant = a1 b2 - b1 a2. A nonzero determinant gives one solution by Cramer's rule. When it is zero, consistency tests distinguish dependent equations from an inconsistent system, including zero-coefficient rows.
Worked example
The equations 0x + 0y = 1 and 0x + 0y = 2 are inconsistent. The equations 0.00000001x = 0.00000001 and 0.00000001y = 0.00000001 have the unique solution x=1, y=1.
Limitations
Calculations use floating-point numbers. Near-singular systems can be sensitive to input rounding; this is not a symbolic algebra system. A tiny nonzero determinant is displayed in scientific notation when necessary.