# Cramer's Rule Linear Equations Solver

This online calculator takes a system of linear equations and applies Cramer's rule to solve it, showing all intermediate steps in the process.

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Created: 2016-10-13 21:25:03, Last updated: 2023-04-04 03:09:03

The calculator for solving systems of linear equations using Cramer's rule takes as input a system of linear equations with the number of equations equal to the number of variables. It then applies Cramer's rule to solve the system, which involves calculating the determinant of the matrix of coefficients for the original system and several modified systems (the formulas can be found below the calculator). The calculator shows the detailed steps for calculating each determinant and then applies Cramer's rule to find the solution for each variable.

#### Cramer's Rule

Digits after the decimal point: 4
System of linear equations

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### Cramer's Rule

You can use Cramer's rule for systems of linear equations where the number of equations is equal to the number of unknown variables, and the coefficient matrix's determinant is not zero (otherwise, the system of equations does not have a unique solution - either it has no solution at all or it has an infinite or parametric solution, and you have to use other methods to find it).

System of linear equations in matrix form looks like this
$AX=B$

If system of linear equations satisfies abovementioned conditions, it has the only solution $(x_{1}, x_{2}, ... , x_{n})$, which can be expressed using this formula
$x_{i} = \frac{\Delta_{A_i}}{\Delta_A}$,
where $\Delta_{A_i}$ – determinant a matrix formed by replacing the i-column values of matrix A with the column of constants (B) values, and $\Delta_A$ – determinant of the original matrix A.

In fact, it is a handy way to solve just one of the variables without having to solve the whole system of equations.

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PLANETCALC, Cramer's Rule Linear Equations Solver