The system of equations are .

To write the augmented matrix,

Place the coefficients of the equations and the constant terms into matrix.

.

Notice that the first element in the second () is 1.

Interchange the rows, so 1 can be in the upper left - hand corner.

To make the first element in the second () row a 0, multiply the first row (R₁) by negative 2 and add the result to row 2().

   (The result is placed in row 2)

To make the second element in the second () row a 1, multiply the second () row by .

     (The result is placed in row 2)

To make the second element in the first () row a 0, multiply the second row (R₂) by negative 2 and add the result to row 1().

      (The result is placed in row 1)

The first row will give you the solution for .

The second row will give you the solution for .

The solution is  .