If f and g are independent of t (which they must be, otherwise I don’t think the concept of zero-isocline makes sense?) then you are just asking to draw contours or level sets of the functions f and g:
using Plots
f(x, y) = x^2 + 2y^2
g(x, y) = x - 2y^3
myrange = -2:0.01:2
contour(myrange, myrange, f, levels=[0])
contour!(myrange, myrange, g, levels=[0])