Solve using elimination. 3/2y+z=3 and -y-2/3z=-2
Rewriting your eqns as,
(3/2)y + z = 3 ----------- (1)
-y - (2/3)z = -2 --------- (2)
multiply (2) by (3/2).
(3/2)y + z = 3 ------------- (3)
-(3/2)y - z = -3 ----------- (4)
Eqns (3) and (4) are the same equation, which means that they are coincident lines, which means that there is an infinite number of solutions, each solution being any point on either line/equation.