3×3 System of Equations Solver

Solve a system of three linear equations in three unknowns (ax+by+cz=d on each of 3 rows) with Cramer's rule to find x, y and z, plus the determinant and uniqueness of the solution.

Input

Enter a system of three linear equations in three variables. Each line is one equation.

On each line, enter "a b c d" separated by spaces or commas (representing ax + by + cz = d).

Coefficients and constants (3 rows)

Result

Solution

x = 2

y = 3

z = -1

Determinant

-1

Uniqueness

Unique

Entered system (coefficient matrix and constants)

2	1	-1	=	8
-3	-1	2	=	-11
-2	1	2	=	-3

How it works

On each row, enter the coefficients a, b, c and the constant d separated by spaces or commas (this represents ax + by + cz = d). Provide three rows.
The determinant of the coefficient matrix is computed with the rule of Sarrus; if it is non-zero, Cramer's rule determines x, y and z uniquely.
When the determinant is zero the solution is not unique (no solution or infinitely many). Review your coefficients.
Cramer's rule finds each variable by dividing the determinant of the matrix with one column replaced by the constants by the original determinant.

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