For the following linear systems enter the letter U if the system has a unique solution, the letter N if it has no solution, and the letter I if it has infinitely many solutions.

. $$\begin{array}{rcrcrcl} x &+& y &+& z &=& 1 \\ 2x &+& 3y &+&4z &=& 1 \\ 3x &+& 5y &+& 7z &=& 1 \\ \end{array}$$
. $$\begin{array}{rcrcrcl} x &+& y &+& z &=& 1 \\ 2x &+& 3y &+&4z &=& 1 \\ 3x &+& 5y &+& 8z &=& 1 \\ \end{array}$$
. $$\begin{array}{rcrcrcl} x &+& y &+& z &=& 1 \\ 2x &+& 3y &+&4z &=& 1 \\ 3x &+& 4y &+& 5z &=& 2 \\ \end{array}$$