Can I write $y$ only in terms of $x$ in the following equation? How would you write $y$ only in terms of $x$ in this equation?
$$x^2 + xy + y^2=100$$

This is a quadratic equation in $y$:
$$y^2+xy+x^2-100=0$$
As such, the quadratic formula gives an expression for $y$ in $x$:
$$y=\frac{-x\pm\sqrt{x^2-4(x^2-100)}}2=\frac{-x\pm\sqrt{400-3x^2}}2$$
