A free variable needs consistency too

Let $Z_1$ and $Z_2$ be two independent discrete random variables such that $Z_1$ follows binomial distribution with parameters n = 2 and p = 1/2, and $Z_2$ follows Poisson distribution with mean 1. Consider the following system of equations with three variables $x_1,x_2$ and $x_3:x_1-2x_2+x_3=1;2x_1-5x_2+2x_3=2;x_1+2x_2+Z_1{x}_3=Z_2$. Then, the probability that the given system of equations has infinite number of solutions equals