System of Equations (3×3)
This solver handles three linear equations a·x + b·y + c·z = d in the unknowns x, y, z. It computes the coefficient determinant D and the three replaced-column determinants Dₓ, Dᵧ, D_z, then reports x = Dₓ/D, y = Dᵧ/D, z = D_z/D.
Frequently asked questions
What method does it use?
Cramer's rule: each unknown equals the determinant with its column replaced by the constants, divided by the coefficient determinant.
What does D = 0 mean?
A zero determinant means the three planes are dependent or inconsistent — either infinitely many solutions or none. The solver reports this without attempting to characterise which case.
How do I enter my equations?
Rewrite each equation in the form ax + by + cz = d and enter the four coefficients per row.