`  Actually I think there is a major flaw in this part of the explanation. It refers to the graphic and talks about visualizing the contour lines of both f and g, but the graphic only shows the contour of f, in blue. The red line for g(x,y)=c is not the contour line of g. If it were, all its points would have the same ``height`` (z coordinate) equal to c, but they vary in height. The red line is in fact the set of points { (x,y,f(x,y)) | g(x,y)=c }. The contour line of g(x,y) = c is, instead, the set { (x,y,c) | g(x,y)=c }.   `