A quadratic equation is defined as an equation in which one or more of its terms is squared but raised to no higher power, having the general form:
where a and b are integral coefficients, and c is a constant.
Your two equations do not meet this criteria (I think). Although one of them is a rectangular hyperbola. See Rectangular Hyperbolas
The other is linear.
The linear equation graphs a line that intersects the 1st quadrant branch of the hyperbola at (1, 3) and (3, 1).
I have seen the term "Simultaneous quadratic systems" in reference to one linear equation and one quadratic equation; also, I have seen it in reference to two quadratic equations. In either case you can have more than one point of intersection (unlike simultaneous linear systems that have at most one point of intersection)
Don't know if this helps. Maybe someone else has a perspective.