How to Use Cramer's Rule

Step-by-Step Guide

1. 1

   Step 1: Know the naming convention.

   In a set of three equations, say 1, 2 and 3, name the coefficients of the equation 1 as: a1, b1, c1.
   
   Name the constant term as d1.
   
   Similarly, name the coefficients of equations 2 and 3 as: a2, b2, c2 and a3, b3, c3 with their constant terms being d2 and d3 respectively. ,,, For finding the value variable x, the first step is to find the determinant of D1.
   
   The matrix D1 is almost the same as matrix D except for the first column having the elements d1, d2 and d3 instead of a1, a2 and a3.,, For finding the value of variable y, the first step is to find the determinant of D2, which is the same as D, except for the second column having the elements d1, d2 and d3 instead of b1, b2 and b3.,, For finding the value of variable z, the first step is to find the determinant of D3 which is the same as D, except for the third column having the elements d1, d2 and d3 instead of c1, c2 and c3.,,
2. 2

   Step 2: Arrange the coefficients in a 3x3 matrix named D. The following steps explain this.

3. 3

   Step 3: Find the determinant of D and note down the value.

4. 4

   Step 4: Find the value of variable x.

5. 5

   Step 5: Find the value of matrix D1 and note it down.

6. 6

   Step 6: Find the value of variable y.

7. 7

   Step 7: Find the value of matrix D2 and note it down.

8. 8

   Step 8: Find the value of variable z.

9. 9

   Step 9: Note down the value of D3.

10. 10

    Step 10: Find the values of variables x

11. 11

    Step 11: y and z. Divide D1/D to get the value of x

12. 12

    Step 12: D2/D to get the value of y and D3/D to get the value of z.

Detailed Guide

About the Author