I had a bit of a disagreement with some of my colleagues over the correct way to represent the solution to a system of two linear equations, e.g.:
\begin{align} x + y = 1\\ 3x + 2y = -1 \end{align}
We should find that the solution is $x = -3$ and $y = 4$. I had been telling my students that they should give the solution as:
x = -3
y = 4
(or really anything that put $x = -3$ and $y = 4$ close together to show the solution compactly--as opposed to just finding the $x$ and $y$ in random parts of their work and never summarizing their findings)
One of my students informed me that another teacher told them that they should give the solution as an ordered pair, i.e. $(-3, 4)$. I explained that yes, assuming that we understand that an ordered pair is $(x, y)$, that that could be a way of representing the solution but that I didn't think it was correct and that giving $x = $ and $y = $ is a more correct way of giving the solution.
I further explained that the ordered pair $(x, y)$ represents a point on a coordinate plane. Thus the ordered pair would be a correct answer if the question had stated something to the affect of "If $(x, y)$ represents points on a coordinate plane, then find the point that represents the solution to the given system of equations." I further elaborated that an ordered pair represents a point, so we can get the solution from the ordered pair (e.g. if we were to solve by graphing), but that the ordered pair does not represent the solution--similar to the idea that the x-intercept is a point and we can get the zeros of a function from its x-intercepts but that an x-intercept does not directly represent a zero of the function.
So my question is whether or not it's proper to represent the solution as an ordered pair when asked to solve a system of two equations or are both ways correct since it's pretty well accepted that ordered pairs are of the form $(x, y)$ (or is it even more correct to give the ordered pair rather than $x = $ and $y = $).