You cannot usefully plot x1 vs t. Your system defines three specific sets of points, two of which are complex-valued
eqn = [x1 == t*x1+x2+t*x3;
sol = solve(eqn,[x1, x2, x3, t], 'maxdegree', 3)
[sol.x1, sol.x2, sol.x3, sol.t]
so the only real-valued solution is x1 about -235, x2 about 732, x3 about -76, and t about 3.1 .
You might perhaps be expecting all-positive results, but look at your equations:
x3 appears with coefficient 1 on both sides, so you can subtract it from both sides, leading to
and if t and x1 and x2 are all positive, then that equation cannot be satisfied. It can potentially be satisfied if t and x2 are both 0
If you substitute t = 0 into your first three equations, you can come out with a consistent solution only if x1 = x2 = x3 = 0. However, that does not satisfied the constraint. This establishes that there is no consistent solution for arbitrary times.