Combining two equations by addition or multiplication?
I have a seemingly simple question concerning the combination of two quadratic equations:
z(x) = x^2 + 2*x - 1
z(y) = 2*y^2 + 3*y + 1
What is the significance of combining these two equations by multiplying them together versus simply adding them together? I know if I take the product of the two equations, I will end up with a 2D surface described by equation z(x,y). But what is the difference between that and the equation obtained by adding them together, z(x,y)?
Any insight on this will be much appreciated.