The four  lines $x+2y=3,3x+4y=7,2x+3y=4$  $4x+5y=6$

$x+2y=3,3x+4y=7$ meet  at (1,1) which does not lie on the other lines.

$\therefore$ The lines are not concurrent The three lines $x+2y-3=0,2x+3y-4=0,4x+5y-6=0$

are concurrent since 

$\left|\begin{array}{ccc}1& 2& -3\\ 2& 3& -4\\ 4& 5& -6\end{array}\right|$$=-18+20-2(-12+16)-3(-2)=0$

They are concurrent at (-1 ,2)and the other line  $3x+4y-7=0$ does not pass through it.