Given the curve defined by the equation $x^2 + xy + y^2 = 7$, find the slope of the tangent line to the curve at the point $(2, 1)$.

Core Concept

Correct. Using implicit differentiation, $2x + y + xy' + 2yy' = 0$. Substituting $x=2$ and $y=1$ gives $4 + 1 + 2y' + 2y' = 0$, which simplifies to $5 + 4y' = 0$, yielding $y' = -5/4$.