Cramer's Rule Calculator - Solve 2x2 and 3x3 Systems

Your details

Choose how many equations are in your system. Both modes use Cramer's rule with determinants.
Coefficient of x in the first equation.
Coefficient of y in the first equation.
Coefficient of z in the first equation (3x3 only).
The right-hand side constant of the first equation.
Coefficient of x in the second equation.
Coefficient of y in the second equation.
Coefficient of z in the second equation (3x3 only).
The right-hand side constant of the second equation.
Coefficient of x in the third equation (3x3 only).
Coefficient of y in the third equation (3x3 only).
Coefficient of z in the third equation (3x3 only).
The right-hand side constant of the third equation (3x3 only).
xUnique solution
2

Solution for x = D_x / D

y3
z-1
Main determinant (D)-1
D_x-2
D_y-3
D_z1
Solution typeUnique solution
x2
y3
z-1

The system has exactly one solution.

  • x = 2, y = 3, z = -1 is the only point that satisfies all three equations simultaneously.
  • The main determinant D = -1 is non-zero, which is what guarantees a unique solution.
  • Substitute the values back into each original equation to verify: the left-hand side should equal the right-hand side exactly.

Next stepTo verify, substitute x, y (and z) back into each original equation and confirm both sides match.

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