By eliminating y, find the solutions to the simultaneous equations.
I've tried many different approaches, come up with 4+ different answers so I have no idea what to do.
When it's expanded and put into standard form we get ......
Solve using your favourite method although this one factorises to .....
From this find your value of x and for each one put the value into either equation to find y.
This is pre-calc rather than calculus and although I don't know how the US system works I'd imagine pre-calc sets you up for calculus. By and large calculus is largely about differentiation (rate of change) and integration (area under a graph). Of course it's far more complicated than that.