The line x = k intersects the graph of the parabola x = -2y^2 - 3y + 5 - y^2 + 9y - 11 at exactly one point. What is k?

k = 15/7

Try simplifying the original equation.

Then find the vertex because that is the only way to intersect at only 1 point.

the vertex is (-3, 1). So k=-3