# Cramer's Rule

This online calculator solves system of linear equations using Cramer's rule and shows detailed steps of the solution

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Created: 2016-10-13 21:25:03, Last updated: 2021-03-02 20:04:44 This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/6007/. Also, please do not modify any references to the original work (if any) contained in this content.

This online calculator solves a system of linear equations using Cramer's rule and shows detailed steps of the solution - substituted matrixes and calculated determinants. Some theory is below the calculator, as usual. #### Cramer's Rule

Digits after the decimal point: 4
System of linear equations

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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

If system of linear equations satisfies abovementioned conditions, it has the only solution , which can be expressed using this formula
,
where – determinant formed by replacing the x-column values with the answer column (B) values, and – coefficient matrix's determinant.

This is Cramer's rule. 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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