How can the solution of an equation be a collection of expressions? Wikipedia says that a solution is an expression or a collection of expressions(one for each unknown) such that, when substituted for the unknowns, the equation becomes an identity.
So far, as I can remember, I've only came across the case of an expression to be a solution. What are some examples where a collection of expressions is a solution to an equation?
One example is the classic parameterization for Pythagorean triples, $a=p^2-q^2$, $b=2pq$, $c=p^2+q^2$, which solve the equation $a^2+b^2=c^2$.
If you have fewer equations than unknowns, you can have expressions for the solution. Say you are given $$x-3y=2z\\ 2x+y=z$$ Given any one variable you can solve for the others, so one way to express the solution is $$y=-3z/7\\ x=16z/7$$