show that $y$ and $x$ can be expressed as a function of $x$ alone in the neighbourhood of the point $(2,1,-1)$

Question

Let $$f(x,y,z)=[x^2-2xz+y^2z^3-7,2xy^4-3y^2+xz^2+5z+2]=(0,0)$$ at $$(2,1,-1)$$ The only method that I have known is the one for solving the homogenous system say for $y$ and $z$ in terms of $x$ but for this question I find it difficult to get the desired result could someone help me the other way of doing it