And that's not the only backup system. Airliners are also equipped with something called a ram air turbine (RAT), inside the belly of the plane. When the plane senses engine failure, the turbine drops from the belly and creates power from the air passing under the plane, as a sort of onboard windmill. Believe it or not, this generates enough energy to run the plane's essential systems like navigation and fly-by-wire, in which the pilot puts commands into the computer system that can control the wings and rudders via hydraulics. You won't have cabin lights, and you may get cut off mid-Big Bang Theory episode, but you'll likely survive. This was how that Airbus that ditched in the Hudson was able to land with no fatalities.
If the plane is forced to run on this minimal power, it will also begin to lose cabin pressure, as that system isn't supported. As the plane descends, those oxygen masks you see in the safety demo will deploy, which have about 10 or 15 minutes' worth of oxygen for everyone on board. By the time that runs out, your plane will likely be below 15,000ft, and the masks won't be necessary.