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Solve linear systems with determinants: each unknown xᵢ = det(Aᵢ)/det(A), where Aᵢ replaces column i with the constants. All intermediate determinants are shown.
2×2/3×3 systems via determinant replacement.
xᵢ = det(Aᵢ) / det(A)
| Symbol | Meaning |
|---|---|
| det(A) | Main determinant (≠ 0 required) |
| det(Aᵢ) | Determinant with column i replaced |
x+y=5, x−y=1: det = −2, Dx = −6, Dy = −4 → x=3, y=2.
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det(A) = 0: the system is dependent or inconsistent — no unique solution.
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Content updated: September 2026