$\"\"$

\

The system of linear equations are $\"\"$ .

\

The system of linear equations can be written as the form of augmented matrix.

\

$\"\"$

\

Perform the operations on $\"\"$ so first column has zeros below its leading 1.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Perform the operations on $\"\"$ so second column has leading $\"\"$ .

\

Multiply the second row by $\"\"$ as follows:

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Perform the operations on $\"\"$ so second column has zeros below its leading 1.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Perform the operations on $\"\"$ so third column has leading $\"\"$ .

\

Multiply the third row by $\"\"$ as follows:

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Perform the operations on $\"\"$ so third column has zeros below its leading 1. \ \

\

$\"\"$

\

$\"\"$

\

$\"\"$ $\"\"$

\

Perform the operations on $\"\"$ so fourth column has leading $\"\"$ .

\

Multiply the fourth row by $\"\"$ as follows:

\

$\"\"$

\

$\"\"$ \ \ $\"\"$

\

Now the matrix is in reduced row-echelon form, and corresponding system is \ \ $\"\"$

\

The value of $\"\"$ substitute in $\"\"$ .

\

$\"\"$ (Substitute $\"\"$ ) \ \ $\"\"$ (Add to each side $\"\"$ )

\

$\"\"$ (Apply LCM rule: $\"\"$ )

\

$\"\"$ (Simplify) $\"\"$

\

The value of $\"\"$ are substitute in $\"\"$ .

\

$\"\"$ (Substitute $\"\"$ )

\

$\"\"$ (Simplify)

\

$\"\"$ (Simplify) $\"\"$

\

The value of $\"\"$ substitute in $\"\"$ .

\

$\"\"$ (Substitute $\"\"$ )

\

$\"\"$ (Simplify) \ \ $\"\"$ (Subtract from each side $\"\"$ )

\

$\"\"$ (Simplify)

\

$\"\"$ (Apply LCM rule: $\"\"$ )

\

$\"\"$ (Simplify) $\"\"$

\

The solution is $\"\"$ , y = 8, z = 2 and its ordered quadruplet is $\"\"$ .