Find the parameter $\displaystyle m$ in order that the system of linear equations:

$\displaystyle x+y+z=2$

$\displaystyle 2x+3y+2z=5$

$\displaystyle 2x+3y+(2m-1)z=2m+1$

a) has one unique solution

b) has no solutions

c) has infinitely many solutions

Thank you