Work out simultaneous equations (3 variables) instantly with clear inputs, formula shown and shareable results.
Cramer's rule extends to three unknowns: each variable equals the determinant of the coefficient matrix with its column replaced by the right-hand side, divided by the coefficient determinant.
Cramer's rule (3×3)
x = det(Aₓ)/det(A), y = det(A_y)/det(A), z = det(A_z)/det(A)
2x + y − z = 8, −3x − y + 2z = −11, −2x + y + 2z = −3 gives x = 2, y = 3, z = −1.
The planes either meet in a line, share a plane, or have no common point. Row reduction is needed to tell which.