According to Kramer's theorem, the necessary and sufficient condition for a system of equations to have a solution is that the coefficient determinant is not 0, that is

|a b|

|d e| not = 0

|a b|

|d e| is a determinant, equal to ae-bd.

Then the solution of the equation is

|c b| |a b| |a c| |a b|

X=|f e| divided by |d e| = 5 y=|d f| divided by |d e|=2.

That is, the determinant obtained by replacing the required unknown column with the right column is divided by the coefficient determinant.

So |c b|

|f e|= 10

For more information, please refer to the knowledge about determinant in linear algebra.