Undergrad Residual of an algebraic equation

[feynman1]

To solve a set of equations f(x,y)=0, g(x,y)=0, where x, y, f, g are scalars, use Newton iteration. At each iteration step i, can certainly define the residual of this set of equations. But what's meant by the term 'residual of x' or 'residual of y'? Not the 'residual of the equations'?

 

[nuuskur]

My guess would be take the residual of the iteration and look at the components separately.