so

. At any max or min in the interior of the set we must have

so one of x= 0, x=y, x=-y must be true. Also

so one of y= 0,

, or

must be true.

If x= 0, only y= 0 satisfies the other equations. If y= x again we have only x= y= 0. I don't see how x= -1/2, y= -1/5 satisfy those equations. I find only x= y= 0.

On the boundary,

,

so we must have

or

and

.

It's never necessary to find

since that is not relevant to the solution. Instead, eliminate

by

**dividing** one equation by the other:

.

That, together with

gives two equations to solve for x and y.