https://www.gregmat.com/quizzes/quiz/prepswift-quant-tickbox-quiz-5-algebra-column-2 (Question 6)
Is it always the case that you need 3 distinct equations for a three variable equation? What if you have two distinct equations for a 3 variable system? Same goes for a four variable system of equations.
Nope, you need at least n total equations. Out of those, you must have exactly n linearly independent equations (equations that provide something new) to obtain a unique solution for n variables.
It is underdetermined; you can either have infinite or no solutions, but never unique ones.
As mentioned above, you need at least 4 equations (containing exactly 4 linearly independent ones) for a unique solution.