#### Solving a system of three linear equations in three variables using Cramer's rule

Example. Solving the system of three linear equations in three variables using

Cramer's rule.

By Cramer's rule:

#### Solving systems of three equations using Gaussian Elimination

Solving a system of linear equations using Gaussian Elimination
Example. Solving the system of three linear equations in three variables using Gaussian Elimination.

Divide the first equation by 3

Multiply (**) by 4 and add -1 times to the second equation, then multiply (**) by (-1) and add to the third equation. We get the following system:

Divide the second equation by

and get

Multiply (***) by

and add -1 times to the third equation.

The system we get

From the third equation z=3. Substitute this to the second equation:

=> y=1>

Substituting y and z to the first equation, we get x

=> x=5

x=5, y=1, z=3