System of Equations Calculator

Your details

A 2x2 system has two equations and two unknowns (x, y). A 3x3 system adds a third equation and a third unknown (z).
Cramer's rule uses determinants; Gaussian elimination uses row operations with back-substitution. Both give the same answer, and the steps panel switches to show whichever method you pick.
When the solution is a simple fraction (e.g. 3/2 rather than 1.5), display it in fraction form.
SolutionUnique solution
x = 1.5, y = 1
x1.5
y1
Determinant (D)-14
Dₓ (x determinant)-21
Dᵧ (y determinant)-14

The two lines cross at exactly one point.

  • The determinant D = -14 is non-zero, confirming one unique intersection.
  • Cramer's rule substitutes each variable's constant column into the matrix and divides by D.
  • Substitute the result back into every original equation to double-check the answer.
= Powered by OnlyCalculators