Consider a system of two equations $f_1(x,y)=0$ and $f_2(x,y)=0$ (that can be nonlinear) with two variables. (it can also be considered in the form of $y=f_1(x)$ and $y=f_2(x)$). Assume that the answer for the system is $(x*,y*)$.
Then, consider another system of equations in which the second equation is replaced with a new equation $f_3(x,y)=0$. If we cannot solve the second system, how can we extract some information about its answer? In particular, I want to know whether the answer for $x$ and $y$ is higher or lower than $x*$ and $y*$. For example, can the different properties of $f_2$ and $f_3$ (e.g., derivation) help?