You don't need to eliminate t in order to find a single function of y=f(x), but rather you have x(t) and y(t) as two parametric functions which define your projectile and you can plot it too.

It means you vary t and calculate x(t) & y(t) that give your projectile.

Assuming:

m=10

v0x=1

v0y=10

beta=3

g=9.8

Trajectory would look like: