At what point on the curve x^2 + y^2 = 9 is the tangent line vertical?

x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3.

This puts the vertices at (-3, 0), (3, 0), (0, -3), and (0, 3).

When is the tangent line vertical? when it passes through the x-axis.

(-3, 0), (3, 0)

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.