Having survived the meteor impact, thanks to some last-minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path. The original equation is y=2x+3.

Question

mathmale · Answer

This is just a fancy (and confusing) way of asking you to determine the solution of the system of equations

$$x^2+y^2=40000~and~y=2x+3.$$  How would you do that?

Hints:  Think:  substitution or graphing are different but still appropriate ways to find the intersection of these two trajectories.

anonymous · Answer

Thanks! I didn't even think about that.