Let $k$ be an [algebraically closed field](/page/Algebraically%20Closed%20Field). Let $F,G\in k[X,Y]$ have positive degrees in $Y$, and set $m:=\deg_Y F$ and $n:=\deg_Y G$. Regard $F$ and $G$ as polynomials in $Y$ with coefficients in $k[X]$, and let $\operatorname{Res}_Y(F,G)\in k[X]$ denote their $Y$-resultant formed with these degrees $m$ and $n$. If $(a,b)\in \mathbb A_k^2$ satisfies $F(a,b)=0$ and $G(a,b)=0$, then $\operatorname{Res}_Y(F,G)(a)=0$. Conversely, suppose $a\in k$ satisfies $\operatorname{Res}_Y(F,G)(a)=0$, and suppose specialization at $X=a$ preserves the $Y$-degrees, meaning $\deg_Y F(a,Y)=m$ and $\deg_Y G(a,Y)=n$. Then there exists $b\in k$ such that $F(a,b)=0$ and $G(a,b)=0$.