Example of Solving a System of Linear Equations by Cramer's Rule.
This solution was made using the calculator presented on the site.
It is necessary to solve the system of linear equations using Cramer's rule.
3  x_{1}  +  3  x_{2}  =  9  
x_{1}  +  2  x_{2}  =  9 
Let's write the Cramer's rule:
x_{1} = det A_{1} / det A
x_{2} = det A_{2} / det A
It is impossible to divide by zero. Therefore, if the determinant of A is zero, then it is impossible to use Cramer's rule.
Let's calculate the determinant A. more info
The determinant A consists of the coefficients of the left side of the system.
3  x_{1}  +  3  x_{2}  =  9  
x_{1}  +  2  x_{2}  =  9 
det A =  3  3  
1  2 
= 3 * 2  3 * 1 = 6  3 = 3
The determinant A is not zero. It is possible to use the Cramer's rule.
Let's calculate the determinant A_{1}. more info
It is necessary to change column 1 in determinant A to the column of the right side of the system.
System  det A  det A_{1}  



det A_{1} =  9  3  
9  2 
= 9 * 2  3 * 9 = 18  27 = 9
Let's calculate the determinant A_{2}. more info
It is necessary to change column 2 in determinant A to the column of the right side of the system.
System  det A  det A_{2}  



det A_{2} =  3  9  
1  9 
= 3 * 9  9 * 1 = 27  9 = 18
Result:
x_{1} = det A_{1} / det A = 9/3 = 3
x_{2} = det A_{2} / det A = 18/3 = 6