(adsbygoogle = window.adsbygoogle || []).push({}); Given that F(x,y)=xy(x+y-1). Determine whether S={(x,y) | F(x,y)=0} is a smooth curve.

Now, F(x,y)=x^{2}y + xy^{2}- xy

Let gradient F = (2xy + y^{2}- y, x^{2}+ 2xy - x) = 0

So 2xy + y^{2}- y = 0 and x^{2}+ 2xy - x = 0

In order to determine where S is smooth, I have to solve these 2 equations for x and y, and I am stuck right here. How can I solve this non-linear system?

Thanks if someone could help me!

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# How to solve this non-linear system?

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