In this video the instructor shows how to solve a 3 x 3 linear system using the Cramer's rule. In this kind of problem you are given three equations in three variables x, y, z and you need to solve for the values of these equations. You can solve this using the Cramer rule which says that the value of x is Dx/D, where Dx and D are two different determinate. Now you have to figure out the determinate to get the value of variable x. The determinate D is called the foundation determinate and is the determinate of matrix that is obtained by the coefficients of x, y and z from the linear equations. Dx is an other determinate whose matrix is similar to the matrix of D but the x coefficients in it are replaced by the values of the equations. Now finally obtain the value of x using the above formula.