A friend of mine has his own little way where you use ratios and shit.

He has got it to work with many a weird thing like your:

x+y=3
2x+y=5

We've been taught to rearrange it, the method is what you'd probably call subbing.

----------

I'll ask him how he does the ratio thing.

Or someone could have fun with a few ratios, and work backwards from the answer of x=2, y=1, which Shinto kindly gave at the start of the equation, meaning we didn't have to work it out.