“Houston, we have a problem!”

You are on a mission from NASA to fix a satellite orbiting the Earth, but on your way there, you went through a comet field and one of the comets punctured a whole in the side of the shuttle and now you are losing fuel! To limit the amount of fuel lost and turn on the emergency fuel supply so you can get back to Earth, you need to flip four switches. However, these switches need to be flipped in a certain order so as not to blow a fuse which would make you lose power completely and not be able to get the emergency fuel that you need. To flip each switch, you need to solve the system of non-linear equations that represents the switch (you can solve them any way). Choose wisely, otherwise you might not get home!