The linear system corresponding to the augmented matrix is

\(x_1—7x_4=8\)

\(x_2+3x_4=2\)

\(x_3+x_4=—5\)

The lending variables are \(x_1, x_2\) and \(x_3\). Solve for the leading variables: \(x_1=8+7x_4\)

\(x_2=2-3x_4\)

\(x_3=—5—x_4\)

Assign arbitrary value to free variable \(x_4\), say \(x_4 = t\). Then the solution set is described by the parametric equations

\(x_1=8+7t, x_2=2-3t, x_3=-5-t, x_4=t\)