Simultaneous linear equations can be easily solved through determinants by the technique called **Cramer’s Rule. **Under this technique the following steps are to be taken up in turn for the purpose:

**Steps:**

i. Construct a determinant of the coefficients of the given variables in the same order as they stand in the equations together with their respective algebraic signs. In doing so, the variables, viz. : x, y, z etc. attached there-with should ignored. Designate this determinant by the capital letter D.

ii. Evaluate the determinant D, and see that its value is not zero. If it is zero, then stop proceeding any further and conclude that the given system of equations is either inconsistent (having no solutions) or dependent (having innumerable solutions). If the det. D is not zero then proceed further as under.

iii. Replace the coefficients of x by the corresponding constants along with their algebraic signs and form a determinant of such transformed coefficients designating the same as the numerator for x variable *i.e., *N x, and find its value in the usual process of expansion.

iv. Replace the coefficients of *y *by the corresponding constants along with their algebraic signs and form a determinant of such transformed coefficients designating the same as the numerator for *y* variables *i.e*., N *y, *and find its value in the usual process of expansion.

v. Replace the coefficients of z by the corresponding constants along with their algebraic signs and form a determinant of such transformed coefficients designating the same as the numerator for z variable i.e., N *z, *and find its value in the usual process of expansion.

vi. Now, for obtaining the values of the different variables, *viz., *x, y and z, apply the following models respectively :

X = (Nx/D), where D ≠ 0

Y = (Ny/D), where D ≠ 0

Z = (Nz/D), where D ≠ 0