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Suppose that you have a system of linear equations in the unknowns \(x\) and \(y\) whose augmented matrix is row equivalent to

\begin{equation*} \left[ \begin{array}{rr|r} 1 \amp 0 \amp 3 \\ 0 \amp 1 \amp 0 \\ 0 \amp 0 \amp 1 \\ \end{array} \right]. \end{equation*}Write the system of linear equations corresponding to the augmented matrix. Then describe the solution set of the system of equations in as much detail as you can.