# How do you solve using gaussian elimination or gauss-jordan elimination, #x +2y +3z = 1#, #2x +5y +7z = 2#, #3x +5y +7z = 4#?

##### 1 Answer

#### Answer:

Write an Augmented Matrix .

Perform Elementary Row Operations, until an identity matrix is obtained.

The solutions will be on the right.

Check.

#### Explanation:

Write

Add row for the equation

Add row for the equation

The augmented matrix is complete. Perform Elementary Row Operations.

We want the coefficient in position

We want the other two coefficients is column 1 to be 0, therefore, we perform the following two row operations:

We want the coefficient in position

We want the other two coefficients in column 2 to be 0, therefore, we perform the following two row operations:

We want the coefficient in position

We want the other two coefficients in column 3 to be 0, therefore, we perform the following two row operations:

We have an identity matrix on the left, therefore, the solutions are on the right:

Check:

This checks.