Solve the second equation for "y=". Then read the slope value off the equation. (It'll be the value multiplied on the "x".)
Differentiate the first equation with respect to x. Set equal to the given slope value, and solve for the corresponding x-value(s).
Plug these x-values into the first equation, and solve for the corresponding y-value(s), and thus the point(s) in question.
(I get the same answer as you've listed.)