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 x-y=-3 to have 3x, you multiply 3 to every term in that equation.
3x-21=-9.
Let's subtract now.
3x-3y=-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.
x-5=-3
x = 2
So x=2, y=5.