# Solving System of Equations Using Cramer's Rule

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The Cramer's Rule is a another method of solving systems of linear equations using determinants. the Cramer's rule is applicable for square matrix and the system must have the same number of equations as variables. It is also important that the determinant of the coefficient matrix must be non-zero.

1. We write the coefficient matrix of the system say matrix A.

2. Now compute the determinant of the coefficient matrix.

3. Let’s consider 1

We will derive the determinant of A

4. Therefore value of x and y will be as follows

x = |A

y = |A

1. We write the coefficient matrix of the system say matrix A.

2. Now compute the determinant of the coefficient matrix.

3. Let’s consider 1

^{st}variable as x and 2^{nd}variable as y. so we can write matrix A_{x}and A_{y}.We will derive the determinant of A

_{x}and A_{y}. which are |A_{x}| and |A_{y}|4. Therefore value of x and y will be as follows

x = |A

_{x}|/|A|y = |A

_{y}|/|A|## Example

Suppose you have entered following equation as A=4, B=4 E=41 and C=44, D=55, F=6

Let’s consider 1^{st} variable as x and 2^{nd} variable as y.

(4)x + (4)y = 41

(44)x + (55)y = 6

The calculator computes the X,Y values as follows:

X = 50.70454545454545

Y = -40.45454545454545