It's been a while since I've posted a math explanation...
Alright, you'll have to subtract those two equations, but you have to make one term (with variable) the same.
Let's allow both equations to have 3x.
3x+2y=16 already has 3x inside, so leave it alone.
So for xy=3 to have 3x, you multiply 3 to every term in that equation.
3x21=9.
Let's subtract now.
3x3y=9

3x+2y=16
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5y = 25
So we have 5y = 25
Divide both sides by 5 and you get y=5.
Plug 5 for y in any equation to get x. I'll use the first one.
x5=3
x = 2
So x=2, y=5.