BALTIC-WAY 2000 Problem 17

Find all real solutions to the following system of equations:

$$\left\{\begin{aligned} x+y+z+t & =5 \\ x y+y z+z t+t x & =4 \\ x y z+y z t+z t x+t x y & =3 \\ x y z t & =-1 \end{aligned}\right.$$